Annu. Rev. Plant Physiol. Plant Mol. Biol. 1989. 40:503 37
Copyright © 1989 by Annual Reviews Inc. All rights reserved
CARBON ISOTOPE
DISCRIMINATION AND
PHOTOSYNTHESIS
G. D. Farquhar, I J. R. Ehleringer, 2 and K. T. Hubick1
~Research School of Biological Sciences, Australian National University,
Canberra, ACT 2601 Australia
2Department of Biology, University of Utah, Salt Lake City, Utah 84112
CONTENTS
INTRODUCTION ..................................................................................... 504
ISOTOPE EFFECTS ........................................................................... ’ ....... 504
ISOTOPIC OMPOSITION A D DISCRIMINATION ....................................... 505
Definitions .......................................................................................... 505
Isotopic Composition of Source Air ........................................................... 507
"’On-line" Measurement of Carbon Isotope Discrimination .............................. 508
THEORY OF CARBON ISOTOPE DISCRIMINATION DURING
PHOTOSYNTHESIS ................................................................................. 508
C3 Photosynthesis ................................................................................. 509
C4 Photosynthesis ................................................................................. 512
C3~ Intermediacy .............................................................................. 514
Crassulacean Acid Metabolism ................................................................. 515
Aquatic Plants and Algae ....................................................................... 516
ENVIRONMENTAL EFFECTS ON CARBON ISOTOPE DISCRIMINATION ......... 517
Light ................................................................................................. 518
Water ................................................................................................ 519
Salinity .............................................................................................. 520
Air Pollution ....................................................................................... 520
WATER-USE EFFICIENCY OF C3 SPECIES ............................................. : .... 520
Transpiration Efficiency and Carbon Isotope Discrimination ............................ 520
Scaling from the Plant to the Canopy ........................................................ 522
Carbon Isotope Discrimination and Plant Growth Characteristics ..................... 523
Genetic Control of Discrimination ............................................................ 524
CONCLUDING REMARKS ........................................................................ 525
APPENDIX ............................................................................................. 525
503
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504 FARQUHAR ET AL
INTRODUCTION
There are two naturally occurring stable isotopes of carbon, ~2C and ~3C.
Most of the carbon is 12C (98.9%), with 1.1% being 13C. The isotopes are
unevenly distributed among and within different compounds, and this isotopic
distribution can reveal information about the physical, chemical, and
metabolic processes involved in carbon transformations. The overall abun-
dance of 13C relative to ~2C in plant tissue is commonly ess than in the carbon
of atmospheric carbon dioxide, indicating that carbon isotope discrimination
occurs in the incorporation of CO2 into plant biomass. Because the isotopes
are stable, the information inherent in the ratio of abundances of carbon
isotopes, presented by convention as ~3C/~2C, is invariant as long as carbon is
not lost. Numerous contributions have been made to our understanding of
carbon isotope discrimination in plants since this area was extensively re-
viewed by O’Leary (97). Here we discuss the physical and enzymatic bases
carbon isotope discrimination during photosynthesis, noting how knowledge
of discrimination can be used to provide additional insight into photosynthetic
metabolism and the environmental influences on that process.
ISOTOPE EFFECTS
Variation in the ~3C/~2C ratio is the consequence of "isotope effects," which
are expressed during the formation and destruction of bonds involving a
carbon atom, or because of other processes that are affected by mass, such as
gaseous diffusion. Isotope effects are often classified as being either kinetic or
thermodynamic, the distinction really being between nonequilibrium and
equilibrium situations. One example of a kinetic effect is the difference
between the binary diffusivity of 13CO2 and that of ~2CO~ in air. Another
example is the difference between the kinetic constants for the reaction of
~2CO~ and 13CO~ with ribulose bisphosphate carboxylase-oxygenase (Rubis-
co). Both these examples are called "normal" kinetic effects in that the
process discriminates against the heavier isotope. Thermodynamic effects
represent the balance of two kinetic effects at chemical equilibrium and are
therefore generally smaller than individual kinetic effects. An example of a
thermodynamic effect is the unequal distribution of isotope species among
phases in a system (e.g. in CO2 in air versus in CO~ in solution).
Thermodynamic effects, like some kinetic ones, are temperature dependent.
Isotope effects, denoted by a, are also called fractionation factors because
they result in fractionations of isotopes. They are here defined (as by some,
but not all chemists) as the ratio of carbon isotope ratios in reactant and
product
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CARBON ISOTOPE DISCRIMINATION 505
Rr
Rp
where R~ is the ~3C/~ZC molar ratio of reactant and Re is that of the product.
Defined in this way, a kinetic isotope effect can be thought of as the ratio of
the rate constants for ~2C and ~3C containing substrates, k~2 and k~3, respec-
tively. Thus
k12 2.
O~kinetic ~ 7"
A simple equilibrium isotope effect would be the ratio of the equilibrium
constants for ~2C and ~3C containing compounds, K12 and K13, respectively:
Diffusional effects belong to the category of kinetic effects, and the isotope
effect is the ratio of the diffusivity of the ~2C compound to that of the
compound. The above effects are discussed more fully in Part I of the
Appendix. Isotope effects may occur at every reaction of a sequence, but the
overall isotope effect will reflect only the isotope effects at steps where the
reaction is partially reversible or where there are alternative possible fates for
atoms, until an irreversible step is reached (97). Kinetic isotope effects
successive individual reactions are usually not additive, but the
thermodynamic ones are. If all reactants are consumed and converted to
product in an irreversible reaction, there is no fractionation. For example,
plants grown in a closed system, where all CO2 was fixed, showed no isotope
effect (6).
ISOTOPIC COMPOSITION AND DISCRIMINATION
Definitions
Farquhar & Richards (39) proposed that whole plant processes should
analyzed in the same terms as chemical processes. From Equation 1 it is
evident that this requires measurements of isotopic abundance of both source
and product. For plants this means measuring Ra (isotopic abundance in the
air) and Rp (isotopic abundance in the plant, where the plant can be considered
the product referred to in Equation 1). For numerical convenience, instead of
using the isotope effect (a = Ra/gp), Farquhar & Richards (39) proposed the
use of A, the deviation of a from unity, as the measure of the carbon isotope
discrimination by the plant:
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506 FARQUHAR ET AL
A = a- 1- Ra--- 1. 4.
The absolute isotopic composition of a sample is not easy to measure directly.
Rather, the mass spectrometer measures the deviation of the isotopic com-
position of the material from a standard,
~p = Rp - Rs = R__.e._ 1,
Rs R~
where Rs is the molar abundance ratio, 13C/12C, of the standard. The reference
material in determinations of carbon isotopic ratios has not normally been
CO2 in air but traditionally has been carbon in carbon dioxide generated from
a fossil belemnite from the Pee Dee Formation, denoted PDB [for which R =
0.01124, (17)]. In this review all compositions that are denoted ~ are with
respect to PDB.
In contrast to 3, the discrimination, A, is independent of the isotopic
composition of the standard used for measurement of Rv and Ra, and is also
independent of Ra. Plants show a positive discrimination (A) against ~3C.
Typically C3 plants have a discrimination of - 20 × 10-3, which is normally
presented in the literature as 20%0 ("per nail"). Consistent with this notation,
we will use %o as equivalent to 10-3. Note that "per mil" is not a unit, and is
analogous to per cent; discrimination is therefore dimensionless. Equations
involving the ~ notation have been made unnecessarily complex by including
the factor 1000 in the definition (i.e. ~p = (Rp/Rs - 1)°1000). We have opted
for simplicity, but the reader should note that factors of 1000 in other
treatments (including our own) should be deleted when comparing to the
equations presented here. Other possible definitions of discrimination are
discussed in Part III of the Appendix.
The value of A as defined above is obtained from 6~ and 6p, where a and p
refer to air and plant, respectively, using Equation 4, and the definitions of $a
and 6p (Ra/Rs - 1; Rp/Rs - 1, respectively):
A-ra-rp 6.l+~,,"
On the PDB scale, free atmospheric CO2 (Ra ~ 0.01115 in 1988) currently
has a deviation, 6a, of approximately -8%o, and typical C3 material (Rp
0.01093) a deviation, 6p, of -27.6%, which yields A = (--0.008 + 0.0276)/
(1 -- 0.0276) = 20.1%~. O’Leary (97) pointed out that the simultaneous
of discrimination and 6 is confusing for work with plants, since the dis-
crimination values (A) are usually positive while those of 8 are usually
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CARBON ISOTOPE DISCRIMINATION 507
negative when PDB is the reference. Where possible, it is preferable to use
molar abundance ratios (R) and compositional deviations (6) only as
termediates in the calculation of final isotope effects (97).
Isotopic Composition of Source Air
The advantage of reporting A is that it directly expresses the consequences of
biological processes, whereas composition, ~p, is the result of both source
isotopic composition and carbon isotope discrimination. This distinction is
particularly important in the interpretation of some growth cabinet work
where the isotopic composition of CO2 can be affected by mixing of CO2
derived from fossil fuel combustion with normal atmospheric CO2. Of course,
it is relevant for vegetation grown near vents outgassing the CO2 produced
from burning underground coal (for which ~ = -32.5%0) (46). Of wider
relevance, the distinction between /~ and A is important when interpreting
results from canopies, if turbulent transfer is poor. In these conditions, there
is a gradient, with height, in isotopic composition of CO2 in the air, ~a. This
gradient occurs because of both canopy photosynthetic activity and soil
respiration and litter decomposition. On the one hand, since photosynthetic
processes discriminate against 13C, the remaining CO2 in air should be
enriched in 13C when CO2 concentration is drawn down (32, 35). On the other
hand, decomposition processes, which release COa with an isotopic composi-
tion similar to that of the decaying vegetation, result in a much lower lac
content of the soil CO2 (1, 68, 116, 122, 123, 148). Francey et al (42)
reported a CO2 concentration of 20 ppm lower, 1 m above the ground, than
outside the canopy in the daylight period in a dense (14 m) canopy of huon
pine in Tasmania. The difference in 3, between the top and bottom of the
canopy was 0.8%°. In warm and dense tropical rainforests, the COz concen-
tration, ca, is large near the forest floor, and 6a is small [ca = 389 ppm, 6a =
-11.4%o at 0.5 m (133); see also (88)]. The isotopic composition, 6a,
CO2 concentration, ca, should be negatively related within a canopy (as in the
above reports) so that for those field-grown plants where the gradients of Ca
are found to be small, the gradient of ~a is also likely to be small.
The isotopic composition of the free atmosphere also changes, slowly
becoming depleted in t3C (41, 45, 70, 92, 108). The progressive decrease
6~ is caused by the anthropogenic burning of fossil fuels (t~ - -26%0). From
1956 to 1982, 6, has decreased from -6.7%0 (at 314 ppm) to -7.9%0 (at
ppm) (70, 92).
There is also an annual cycle of 10 ppm in c,, and 0.2%° in 3a, in the
northern hemisphere, associated with seasonal changes in standing biomass;
the amplitudes of changes in c,~ and 6,, are much smaller in the southern
hemisphere (92). In major metropolitan areas, ~,~ may vary by as much as 2%0
both daily and annually, because of human activities (64, 65). Throughout
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508 FARQUHAR ET AL
this review when discussing studies where isotopic composition of plant
material is presented without corresponding measurements of 8a; we also
provide an estimate of discrimination (A) using the assumption (for field-
grown plants) of an atmospheric composition (Sa) of -8%°.
"On-line" Measurement of Carbon Isotope Discrimination
In most studies, composition of CO2 from combustion of plant material (Sp)
has been compared to that of the atmosphere in which the material was grown
(Sa) to yield an average discrimination over the period in which the carbon
was fixed. A more direct and nondestructive means of measuring short-term
carbon isotope discrimination is to measure the changes in the 13C/~2C ratio of
the CO2 in air as it passes a leaf within a stirred cuvette, such as those
commonly used for whole-leaf gas-exchange measurements (32, 36, 62,
125). If the reactions associated with photosynthetic CO2 fixation dis-
criminate against 13C, the remaining CO2 should be enriched in 13C. Dis-
crimination can be calculated from measurements of the concentration (c) and
the isotopic composition (~5) of the CO2 of the air entering (ce and ~Se)
leaving (Co and tSo) the cuvette according to an equation derived by Evans et al
(32),
1 + 8o -- ~(8o- Be) 7.
where ~ = Ce/(Ce-Co). Note that Evans et al (32) used the constant 1000 in the
denominator ather than 1, because their values of ~ had also been multiplied
by 1000.
O’Leary et al (102) used a different "on-line" technique, where the plant
was enclosed in a bell jar and allowed to deplete the CO2. The continuing
isotopic enrichment of the remaining CO2 was monitored and discrimination
calculated from a set of differential equations.
Estimates from these "on-line" methods are usually comparable to those
from tissue combustion analyses (32, 62, 125). The clear advantage over
tissue combustion of the "on-line" approaches is that they are nondestructive
and rapid (-- 30 rain), permitting studies of isotope discrimination as
function of time or of physiological and environmental conditions, The
measurement of tissue is of course invaluable for longer-term integration, and
for the ease with which small amounts of material can be collected, stored,
and subsequently analyzed.
THEORY OF CARBON ISOTOPE DISCRIMINATION
DURING PHOTOSYNTHESIS
Carbon isotope composition of plants was first used to indicate photosynthetic
pathways in plants (2, 3, 89, 93, 106, 120, 127, 128, 130, 144, 145, 150,
151, 156, 159, 160, 163). This is because phosphoenolpyruvate (PEP)
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CARBON ISOTOPE DISCRIMINATION 509
carboxylase, the primary carboxylating enzyme in species having a C4
metabolism, exhibits a different intrinsic kinetic isotope effect and utilizes a
different species of inorganic carbon that has an isotopic composition at
equilibrium different from that of Rubisco. Isotopic screening was a simple
test for determining the photosynthetic pathway when it was unknown for a
species. Over the past 15-20 years, the results of such surveys have provided
a broad base of the distribution of photosynthetic pathways among different
phylogenetic groups and ecological zones (97, 99, 106). Although major
photosynthetic groups could clearly be distinguished by their isotopic com-
position, the results of these early studies also indicated that there was
substantial variation in isotopic values at both the interspecific and in-
traspecific levels, as well as variation associated with different environmental
growth conditions and with variation in dry-matter composition. Substantial
theoretical and experimental progress has been made over the past ten years in
understanding the biochemical, metabolic, and environmental factors con-
tributing to the different isotopic compositions among plants. The major
isotope effects of interest are listed in Table 1 and include kinetic discrimina-
tion factors associated with diffusion (denoted by a) and enzyme fractionation
(denoted by b), as well as equilibrium discrimination factors (denoted by
We refer to this table as we review the theory and supporting evidence.
C3 Photosynthesis
HIGHER PLANTS everal models have been developed to describe the
fractionation of carbon isotopes during Ca photosynthesis (38, 69, 97, 109,
122, 149). The models are similar in structure, each assuming that the major
components contributing to the overall fractionation are the differential dif-
fusivities of C02 containing lec and ~3C across the stomatal pathway and the
fractionation by Rubisco. Each of the models suggests additivity of fractiona-
tion factors weighted by .,the relative "limitation" or CO2 partial pressure
difference imposed by the step involved. Of the models, that of Farquhar et al
(38) has been the most extensively developed and tested. Their expression for
discrimination in leaves of C3 plants in its simplest form is,
A a Pa -- Pi q_ b Pi
=
--= a + (b- a) P__L, 8.
Pa Pa l)a
where a is the fractionation occurring due to diffusion in air (4.4%0,
theoretical value that has not been confirmed experimentally), b is the net
fractionation caused by carboxylation (mainly b3, discrimination by Rubisco;
see Table 1 and also Part IV of the Appendix) and p,, and p; are the ambient
and intercellular partial pressures of CO2, respectively. Equation 8 is derived
in Part II of the Appendix; see also reference 5.
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510 FARQUHAR ET AL
Table 1 Isotope effects of steps leading to CO2 fixation in plants.
Isotope effect Discrimination
Process (,~) (%~) Symbol Reference
Diffusion of CO2 in air through 1.0044
the stomatal porea
Diffusion of CO2 in air through 1,0029
the boundary layer to the
stomataa
Diffusion of dissolved CO2 1.0007
through water
Net Ca fixation with respect 1.027
to p~
Fixation of gaseous CO2 by 1.030 (pH = 8)
Rubisco from higher plants 1.029 (pH = 8.5)
Fixation of HCO~- by PEP 1.0020
carboxylase 1.0020
Fixation of gaseous CO2 (in equi- 0.9943
librium with HCO~- at 25°C)
by PEP carboxylase
Equilibrium hydration of CO2 0.991
at 25°C 0.991
Equilibrium dissolution of CO2 1.0011
into water 1.0011
4.4 a Craig (16)
2.9 ab Farquhar (33)
0.7 a~ O’Leary (98)
27 b Farquhar & Richards
(39)
30 b3 Roeske & O’Leary
(119)b
20 b3 Guy et al (50)
2.0 b4* O’Leary et al (101)
2.0 Reibach & Benedict
(117)
-5.7 b4 Farquhar (33)
-9.0 eb Emrich et al (31)
-9.0 Mook et al (91)
1.1 .e, Mook et al (91)
1.1 O’Leary (98)
Theoretical value
bData corrected for dissolution of CO~
The significance of Equation 8 is that when stomatal conductance is small
in relation to the capacity for CO2 fixation, p; is small and A tends towards
4.4%0 (see Figure 1). Conversely, when conductance is comparatively large,
pi approaches Pa and A approaches b (perhaps 27-30%0; see Appendix Part
IV). Nevertheless, it is a little dangerous to take the argument further and say
that when Pi and A are small, stomata are necessarily limiting photosynthesis.
That conclusion would only follow if the relationship between assimilation
rate, A, and p; remained linear beyond the operational point (40).
There are several cases where measurements of both A and PdPa have been
made in controlled conditions. Farquhar et al (35) found a significant correla-
tion between A in dry matter and discrete measurements of Pi/P, among
different species over the range of p~/pa 0.3-0.85. The best fit, taking a as
4.4%0, was observed with a value for b of 27%0. The leaf with the lowestpi/p,
was from an Avicennia marina plant, which showed discrimination of 11.8%0.
Such low values of A had previously been considered to be in the range of C~
plants. Downton et al (using spinach; 21) and Seemann & Critchley (using
beans; 124) also observed significant correlations between A in dry matter and
p~/p~, the best fit being obtained by setting b equal to 28.5%0 and 26.4%0,
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CARBON ISOTOPE DISCRIMINATION 511
3O
2O
10
4
0
C3 ¯
C4 o
._
i~11
0 0.2 0.4 0.6 0.8 1.0
Pi / Pa (,bar / bar
Figure 1 Carbon isotope discrimination, A, versus the ratio of intercellular and ambient partial
pressures of CO2, P~/Pa, wl~en all are measured simultaneously in a gas exchange system (36).
The line drawn is Equation 8 with a = 4,4%¢ and b = 27%c.
respectively. However, it should be noted that in none of the above studies
was ~ directly measured. Winter (155) showed that both A and Pi/Pa of leaves
became smaller as Cicer arietinum plants were water stressed. Conversely,
Bradford et al (9) showed that both were greater in a tomato mutant lacking
abscisic acid (ABA) than in its isogenic parent. Phenotypic reversion of A and
Pi/Pa occurred when the mutant was sprayed with ABA during its growth.
Measurements of mistletoes and their hosts (25, 30) showed interspecific
variation in both A and Pi/Po. Guy et al (52) found that increased salinity
decreased A in Puccinellia and Pi/Pa as expected from theory. Over the short
term, Brugnoli et al (11) showed that the assimilation-weighted value ofpi/pa
and A of sugar produced by a leaf in a single day followed the predicted
theoretical relationship (Equation 8) with a fitted value for a of 4.1%o and for
b of 24--25.5%0. The overall discrimination to starch appeared to be slightly
smaller. In all of the above cases, A, inferred from the carbon composition of
leaf material, and pi/Pa were positively correlated. The values of b that gave
the best fit showed variation, which could have many causes (see Part IV of
the Appcndix for further elaboration).
NONVASCULAR PLANTS urveys of isotopic composition have been made
on species of mosses, liverworts, and lichens. Isotope ratio variation in the
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512 FARQUHAR ET AL
range of -21.3%o to --37.5%0 (A = 13.6-30.4%o) has been reported (121,
128, 135, 136).
For mosses, and some liverworts, the gametophytes are morphologically
similar to higher plants but are restricted in size by their lack of vascular
tissue. Their leaflike photosynthetic structures tend to be just one cell layer
thick and do not have the specialized anatomy of higher plants. They do not
consistently have an epidermis with impermeable cuticle and stomata, so we
might not expect to observe variation in isotope discrimination arising from
short-term variation in permeability to gases as with higher plants. It is
possible, however, that permeability changes with water content. Even if this
resistance remains constant, the gradient in partial pressure across it will
change if the flux changes. For example, assimilation rate may change
because of differing light levels, and this should increase the gradient and
decrease A (32). For other liverworts with a thicker thallus and an epidermis,
there may be pores that lead to air chambers, like stomata in higher plants,
and we would expect to see variation in discrimination similar to that in higher
plants.
In contrast to our explanations for variation in A in mosses and liverworts,
Rundel et al (121) attributed the very negative values of/Sp in mosses in humid
conditions to a large content of lipid in the tissue of those species [as lipids are
depleted in ~3C compared to other plant compounds (97)]. Teeri (135)
gested that these differences may have arisen because of differences in the
amount of carbon fixed by PEP carboxylase, but this is unlikely to differ from
that in higher plants.
Among lichens, there are differences in carbon isotope discrimination that
depend on the phycobionts in the symbiotic association (74, 76). Green algae
as phycobionts are able to maintain positive photosynthetic rates when only
misted, whereas when cyanobacteria are the phycobionts, surface liquid water
is required for photosynthetic activity (75). This difference suggests that the
CO2 diffusion rate may be limiting when cyanobacteria are the phycobionts;
correspondingly, the carbon isotope discrimination by lichens with cyanobac-
teria is 2-4%0 less than that of lichens with green algae. Another possibility is
that liquid water is needed for a bicarbonate transport system, which also has
a characteristically smaller discrimination (see the section below on algae).
further complication is that discrimination by Rubisco, b3, is 21%o in the only
cyanobacterium measured compared to 29%o in higher plants (50). A great
deal more work is required before an equation like Equation 8 could be
applied with confidence to lichens.
C4 Photosynthesis
Variation in isotopic composition among plants with the C4 photosynthetic
pathway is less than in C3 plants, because the term b from Equation 8 (largely
reflecting b3, the discrimination by Rubisco, ~ 30%0) is replaced by (b4
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CARBON ISOTOPE DISCRIMINATION 513
b3~b) which is numerically much smaller than b3. This is because b4 (the
effective discrimination by PEP carboxylase) is - -5.7%0 (see Table 1)
~b [the proportion of the carbon fixed by PEP carboxylation that subsequently
leaks out of the bundle sheath, thereby allowing limited expression of Rubisco
discrimination (b~)] is necessarily less than unity (33). The bases for
model of discrimination are as follows: CO2 diffuses through stomata to the
mesophyll cells, where it dissolves (es) and is converted to HCO~- (eb). At
equilibrium, the heavier isotope concentrates in HCO~- compared to gaseous
CO2--i.e. the combined terms es + eb are negative (Table 1). In turn, PEP
carboxylase discriminates against Hl3CO£----i.e. b$ is positive and normal for
a kinetic effect. Thus if the gaseous intercellular CO2 is in equilibrium with
HCO~-, then the net discrimination from CO2 to OAA is
b4 = es + eb + bf[ 9.
which is negative because of the magnitude of eb. Various transformations
then occur, depending on Ca subtype, but the net result in all cases is that CO2
is released within the bundle sheath cells and refixed by Rubisco. There is
little opportunity for discrimination in the release of CO~ in the bundle sheath
cells because of the lack of significant biochemical branches. No further
discrimination would occur if the bundle sheath were gas tight (153). Howev-
er, some quantities of COz and HCO~- are likely to leak out of these cells and
into the mesophyll cells, especially through the apoplastic portions of the
bundle sheath cells, where they can then mix with other CO2 that has diffused
in through the stomata. The leak is a branch from the main path of carbon and
allows some discrimination by Rubisco in the bundle sheath cells (bs).
Various models (18, 33, 56, 110, 117) have addressed aspects of the ~3C
discrimination during C4 photosynthetic metabolism. Intrinsic to all of these
models is the notion that variation in isotopic composition in Ca plants is
associated with leakage of C02 and/or HCO~-. The "leakiness" (~b) may also
be regarded as a measure of the "overcycling" by PEP carboxylase that occurs
in mesophyll cells, raising the partial pressure of CO~ within the bundle
sheath cells (33).
Farquhar (33) developed an expression for the discrimination occurring
Ca photosynthesis, in which
A= a Pa -Pi + (b4 + b3~b) __Pi = a + (b4 + b3~ - a) --.Pi 10.
Pa Pa Pa
Depending whether (b4 + b~,;b - a) is positive, zero, or negative, the
dependence of A on Pi/P,~ will be positive, zero, or negative. Experimental
evidence suggests that the factor is often close to zero, with short-term
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514 FARQUHAR ET AL
discrimination responding little to variation inpi/Pa (32, 36, and see Figure 1).
From Table 1 it may be seen that the zero value is obtained with ~b = 0.34.
Farquhar (33) and Hattersley (56), using the Farquhar model, predicted
bundle sheath "leakiness" above (k = 0.37 (the value differs from 0.34
because a smaller value was assumed for b3) should result in a positive
response of A to increasing Pi/Pa. Anatomical variations between C4 types
(55) may be associated with variations in ~b. For example, Ehleringer
Pearcy (29) observed that quantum yields for CO2 uptake are lower for all
dicots and NAD-ME (malic enzyme) C4 type grasses than for NADP-ME
PCK (phosphoenolpyruvate carboxykinase) types, which have bundle sheaths
with suberized lamellae (12, 57). Diminished quantum yields are to
expected as a result of increased leakiness--i.e, increased overcycling within
the mesophyll cells. The measured differences in carbon isotope discrimina-
tion by NAD-ME, NADP-ME, and PCK type Ca grasses as deduced from
isotopic composition (10, 56, 150, 163) and from "on-line" measurements
(32, 36) are consistent with the expectation that leakage is greatest in the first
type. Because th is a measure of the overcycling as a proportion of the rate of
PEP carboxylation, it is likely that A will increase whenever Rubisco activity
is diminished more than PEP carboxylase activity by some treatment. Thus ~b
and A depend as much on coordination of mesophyll and bundle sheath
activity as on anatomical features.
C3-C4 Intermediacy
Monson et al (90) measured isotopic composition of C3-C 4 in termediate
species in Flaveria and reported A values of 9.6-22.6%0. They suggested that
the isotopic variation resulted from differences in bundle sheath leakage
(according to Equation 10). While this probably accounts for some of the
variation, another biochemical factor may also be important. The C3-C4
"intermediate" species appear to have glycine decarboxylase confined to the
bundle sheath cells (63, 115). The effect is that CO2 released by photorespira-
tion is released and partially refixed in the bundle sheath, so that discrimina-
tion by Rubisco can occur twice (S. von Caemmerer, unpublished). The
modification to b, the C3 carboxylation parameter from Equation 8, is thus the
product of the proportion, As~A, of carbon fixed twice (where As is the rate of
assimilation in the bundle sheath, and A that by the whole leaf), and ~b, the
proportion of the carbon supplied to the bundle sheath that leaks out. In the
simplest form the equation becomes (G. D. Farquhar, unpublished)
A=aP"-P’~-~+b(l +pa chA~]Pi =a +[b(1A ]Pa + ~-~-~-~) -OIpj’jpO 11.
This theoretical prediction awaits experimental testing.
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CARBON ISOTOPE DISCRIMINATION 515
Crassulacean Acid Metabolism
The details of Crassulacean acid metabolism (CAM) that affect A have been
recently reviewed by O’Leary (99). In this section, we present equations for A
analogous to those discussed earlier for C3 and Ca carbon assimilation path-
ways. Plants in the full CAM mode take up CO2 and synthesize oxaloacetate
using PEP carboxylase, and the oxaloacetate (OAA) is then reduced and
stored as malate (103). At dawn the plants close their stomata and de-
carboxylate the malate, refixing the released CO2 using Rubisco. The malate
that is stored at night will show the same discrimination as for Ca species with
zero leakage (33), i.e.
A= a + (b4 - a) --.Pi 12.
Pa
Winter (154) reported that nocturnal values of Pi/Pa in Kalanchoe pinnata
started at a Ca-like value (- 0.4) and increased with time to a C3-1ike value
(- 0.7) before dawn. On this basis, we could expect instantaneous A of the
carbon being fixed to have decreased from -- 0.4 to -2.7%~ as the night
progressed. This is consistent with observations that A of crystalline oxalate
and of carbon-4 of malic acid were near to zero (58, 100).
If the stomata closed completely at dawn, the photosynthetic tissue would
form a closed system and there would be no fractionation of the carbon
between malate and the sugar products. However, consider the case where the
stomata were not closed in the light while a CAM plant was enclosed in a
cuvette with no external CO2. In this case, there should be a discrimination in
going from malate to the new C3 carbon because we no longer have a closed
system. The discrimination is given by 4,(b3 - a), where 4, is the proportion
of decarboxylated carbon that leaks out of the leaf. Nalborczyk (94) allowed
CAM plants to fix CO2 only at night and found that the overall discrimination
was -- 3%0. This result implies that 4’ was about 0.05--0.15. However, when
CAM plants are growing in normal air, evolution of CO2 in the light is usually
negligible.
Toward the end of the light period, after decarboxylation of all the stored
malate, there is sometimes CO2 uptake [denoted phase IV by Osmond (103)]
via Rubisco, and possibly involving PEP carboxylase as well. Nalborczyk et
al (95) allowed plants to fix carbon only in the light and observed a dis-
crimination of 21%~, which is what one would expect with a typical C3 value
of P~/Pa in Equation 8.
Therefore in the simplest case of C4 fixation in the dark and Ca fixation in
the light, the average discrimination over a 24 hr period is
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516 FARQUHAR ET AL
fD dt dtA(b4 - a) + __ A(b - a)
Pa ~ PaA=a+
f°Adt ÷ f~ dt ’ 13.
where A is the assimilation rate, fDdt denotes the time integral in the dark,
and fLdt that in the light, and b for the light period is the average of b~ and b4
weighted by the rates of RuBP and PEP carboxylation (if the latter occurs),
respectively.
Aquatic Plants and Algae
Carbon isotope combinations measured in aquatic plants range between
-11%~ and -39%0, potentially leading to the mistaken impression that both
C3 and Ca photosynthetic pathways are present in aquatic plants (4, 22, 105,
113, 132). However, with limited exceptions (86, 147), C4 plants are
known from aquatic habitats. When CO~ fixation is via the normal C3
pathway, Equation 8 applies, but with the parameter a modified to reflect
diffusion in the aqueous phase (es + al) so that
A = (es + a~) p’~ -- p’-~--~ + b Pc. = e., + a~ + (b - es - a~) P--f--~, 14.
Pa P, Pa
where the equivalent partial pressure of CO2 at the site of carboxylation is
denoted as Pc. Note that the discrimination during diffusion of CO2 in water
(at) is 0.7%0 (98) and not 11%o as some authors have-written. Much of the
diffusion of inorganic carbon in the aqueous environment will be as bicarbon-
ate rather than CO2, but the discrimination here should also be small (38).
Note further that the discrimination is with respect to gaseous CO2 in equilib-
rium with the aqueous environment.
However, there is a widespread mechanism(s) among marine and freshwa-
ter organisms for raising the concentration of CO2 at the site of carboxylation
above that of the environment (5, 80). Farquhar (33) suggested that
equation for C4 discrimination could be adapted to describe discrimination if
the active species transported is bicarbonate as
A = (es + ai)p~ - p~ + (e~ + eb +bm + b3~b) p--Lc
= es + at + (eo +bm + b3qb - at) P-~-~, 15.
P,
where bm is the fractionation during membrane transport. The value of bm is
unknown, but it has been cautiously assumed to be small, making (e~ + eb +
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CARBON ISOTOPE DISCRIMINATION 517
b~n), which is the analog for b4 from the C4 model, close to -7.9%~ (33). Note
that in both Equations 14 and 15 the discrimination is again expressed in
relation to a gaseOus source. As with Equation 14, the discrimination in
relation to dissolved COz as the source, provided it were in equilibrium with
the gas phase, would be found by subtracting es and with reference to
bicarbonate (again, if in equilibrium) would be found by subtracting es + eb.
However, it is convenient to retain the same convention for source carbon as
used for aerial plants (i.e. gaseous COz), especially when we have chosen
gaseous CO~ as our substrate for carboxylation by Rubisco (see definition of
b3 in Table 1). The latter choice is also reasonable in a mechanistic sense
because the Rubisco site, with RuBP bound, probably reacts with gaseous
substrates only.
The effects on A of induction of active carbon accumulation were elegantly
demonstrated by Sharkey & Berry (125). The green alga Chlamydomonas
reinhardtii was grown at 5% CO2 and then transferred to normal air levels of
CO2. Before transfer, A was 27-29%0, and after 4 hr of induction A was 4%0.
Sharkey & Berry (125) discussed their results in terms of slightly simplified
versions of Equations 14 and 15. Berry (5) noted that measurements of A
alone are insufficient to distinguish between a CO2 concentrating mechanism
(Equation 15) and a normal C3 mechanism (Equation 14) with a large
resistance to diffusion. In both cases, A is small because most of the COz
reaching Rubisco is fixed.
ENVIRONMENTAL EFFECTS ON CARBON ISOTOPE
DISCRIMINATION
Goudriaan & van Laar (47), K6rner et al (72), and Wong et al (161)
among the first to note a strong correlation between the photosynthetic rate
and leaf conductance. This correlation was maintained over a wide variety of
plant species and under a diversity of environmental treatments, implying
some level of regulation between COz demand by the chloroplasts and COz
supply by stomatal control. If in fact there were no deviations from the slope
of the photosynthesis-versus-conductance relationship and if the intercept
were zero (as was the case in the original papers), then the intercellular CO2
pressure (Pi) of all plants would have been constant, dependent only
photosynthetic pathway. This constancy was mistakenly suggested in at least
one early review (126). Although a number of studies that followed showed
significant tendency for photosynthesis and conductance to be correlated
(161), many of these data sets exhibited some deviation from a linear relation-
ship or a nonzero intercept (112, 152). It is unfortunate that in the search for
general patterns the variance in Pi was, for a time, ignored. When it was
recognized that there was a fundamental relationship between A or 6p and Pi,
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518 FAI~QUHAR ET AL
more effort was put into documenting and understanding the isotopic variation
at both the environmental and genetic (intra- and interspecific) levels. In the
next sections, we describe what is known about the relationship betweenpi (as
measured by isotope discrimination) and environmental parameters.
Light
While some of the first experiments reported no consistent pattern between
leaf isotopic composition, ~p, and irradiance (129), later studies have in-
dicated that ~p increased with an increase in growth irradiance. Interpretation
of carbon isotope composition of leaves experiencing different light levels has
been somewhat controversial. The controversy lies in separating the effects of
light on discrimination from correlated effects on ~Sa (source air), both
which affect leaf carbon isotopic composition. In field studies, Vogel (148)
was among the first to describe a consistent pattern of isotopic variation in
leaves under canopy conditions where light levels varied substantially. He
noted that 8p within a canopy decreased by 3%0 between the top (19 m) and
bottom (1 m) of the canopy. He further noted that the isotopic composition
soil CO2 was approximately - 19%o, while that of the atmosphere was only
-7%0. He attributed all of the decrease in ~5e of leaves at lower layers to a
recycling of soil CO2 (a lighter source CO2), although the isotopic composi-
tion of CO2 within the canopy, ~Sa, was not measured. He calculated that
recycled CO2 accounted for 15% of the carbon incorporated in lower leaf
layers--assuming that the physiological discrimination was constant. Medina
& Minchin (87) pursued these observations, reporting ~;13C gradients of 4.7
and 5.6%o between upper and lower canopy leaves for two different tropical-
forest types. Again the decrease in dil3C of leaves at lower levels was
attributed to a lighter source CO2, with the implication that as much as 20% of
the carbon fixed in lower leaf layers was derived from soil respiration. A third
study by Schleser & Jayasekera (122) reports a similar pattern for fores~
beech and isolated lime trees. Again, they attributed this result to recycled
soil CO2.
Some recent studies have examined both ~Sa and ~e- In their study in a huon
pine fores’t, Francey et al (42) observed that ,Sp decreased with canopy deptti,
but without ~;a decreasing in a corresponding manner, which indicates a
.physiological effect. They found that leaves from lower in the canopy had
greater p~ values than those from the upper canopy, suggesting, according to
Equation 8, a greater discrimination in lower leaves. Ehleringer et al (27, 28)
observed a similar pattern with ten shrub and tree species from a subtropical
monsoon forest. Leaf ~5e decreased (i.e. became more negative) and p~ in-
creased as observations were made deeper in the canopy. Furthermore, when
only outer canopy leaves were measured on plants with differing degrees of
canopy closure, ~p was decreased with decreasing irradiance, consistent with
the model of increasing p~ at lower light levels. These measurements were
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CARBON ISOTOPE DISCRIMINATION 519
confirmed with gas exchange observations of the dependence of Pi on irra-
diance. While it is undoubtedly true that a fraction of the soil CO2 is
incorporated within leaves at the lower canopy level, much of the decrease in
leaf isotopic composition is likely to be associated with stomatal and
photosynthetic effects. Higher Pi values in understory leaves are likely to
benefit plant performance when leaves are exposed to higher irradiances
during sunflecks and when leaves are allowed to operate at higher quantum
yields (71, 107). In the field, effects of irradiance on pl are difficult
separate from those of leaf-to-air vapor pressure difference (vpd). The smaller
vpd at the bottom of the canopy could also cause greater p~, and greater A
(another complication is discussed after Equation A13 in the Appendix).
Water
PHYSIOLOGICAL RESPONSE TO DROUGHT When soil moisture levels are
decreased, a common response is simultaneous decreases in photosynthesis,
transpiration, and leaf conductance (40). If the "supply function" of photo-
synthesis (leaf conductance) decreases at a faster rate under stress than the
"demand function" [photosynthetic dependence on Pi, sensu Farquhar &
Sharkey (40)], then p~ will decrease. This effect should be measurable
either an increase in 6p or correspondingly as a decrease in A. Over the short
term when new growth has not occurred, the impact of stress can be detected
in carbohydrate fractions within leaves (11, 163a, 81). Alternatively, the
reduction in pi/Pa can be measured using the "on-line" approach (62).
longer-term observations under both growth-chamber and field conditions,
plants under water stress induced by low soil moisture availability produced
leaves with lower Pi values as estimated by carbon isotopic composition (19,
23, 26, 39, 59-62, 131, 140, 155). Increasing the soil strength (physical
resistance to root penetration), such as might occur in drier soils, induces
reduction of A, as observed with reduced soil moisture levels (84).
An increase in the leaf-to-air vapor pressure difference will also cause
diminution ofpi and A in the short term (11) and long term (35, 39, 157).
PHOTOSYNTHETIC PATHWAY SWITCHING In response to changes in leaf
water status, a number of species show dramatic shifts in carbon isotope
composition (up to 10--15%o) associated with changes in photosynthetic
metabolism. Thus upon exposure to increased drought, some species can shift
from C3 to CAM photosynthesis (8, 54, 67, 78, 137-140, 146, 158). Corre-
spondingly, there is an increase in ~p (decrease in A). This shift in metabolism
is reversible, dependent primarily on plant water status, and can occur in both
annual and perennial leaf succulents of arid habitats. Other plants, notably
"stranglers" of tropical habitats, exhibit CAM metabolism as epiphytic ju-
veniles, but later switch to Ca metabolism when roots reach the soil surface
(111, 134, 143).
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520 FARQUHAR ET AL
PHOTOSYNTHETIC TWIGS AND STEMS In an interesting twist on the photo-
synthetic-shift theme, at least two stem succulents native to southern Africa
exhibit C3 metabolism in the leaves (which are shed early in the drought
period) and CAM in the stems (77, 142). In recent studies on green-twig
plants from arid lands of North America, high rates of photosynthesis have
been observed in twig tissues that are comparable to those observed in leaves
(13, 24, 104, 131). Unlike the previous example, the twigs of these species all
have C3 photosynthesis. In all such species examined to date, Pi values as
measured by gas exchange techniques are lower in twig than leaf tissues,
leading to a significant difference in carbon isotopic composition of the two
tissue types. Thus, in these cases, the decrease in h of the twigs is associated
with increased diffusional constraints rather than with a change in metabolic
pathway as described in the previous section.
Salinity
In nonhalophytic species, increased salinity has numerous metabolic effects
(48). Stomatal closure is typically associated with increased salinity (20,
79, 124). Thus it should not be surprising to note that in those species A
decreased with increasing salinity, indicating a decrease in pi with increasing
stress (124). What is perhaps more intriguing is that halophytic species also
exhibit a similar pattern whether in field or laboratory conditions (35, 51-53,
96, 163a).
Air Pollution
A long-term consequence of exposure to air pollutants (e.g. ozone, sulfur
dioxide) at the leaf level is normally a decrease in both leaf conductance and
photosynthesis (118). It is not clear, however, whether this decrease in gas
exchange represents overall decline in metabolic activity or an increased
diffusion limitation imposed by stomata. In each of the limited number of
studies available that examine carbon isotope discrimination by leaves of
plants exposed to pollutants, exposed plants exhibited lower A values,
suggesting lower Pi (43, 49, 81). Changes in isotopic composition of leaf
tissues from these studies of 1%o or greater were common even under modest
exposures to air pollution. Under long-term, chronic exposure to air pollut-
ants, clear differences exist in the carbon isotope ratios of the wood of annual
growth rings that are consistent with short-term,-leaf-level observations (43,
44, 81).
WATER-USE EFFICIENCY OF C3 SPECIES
Transpiration Efficiency and Carbon Isotope Discrimination
Measurements of A in C3 species may usefully contribute to the selection for
transpiration efficiency--i.e, the amount of carbon biomass produced per unit
water transpired by the crop.
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CARBON ISOTOPE DISCRIMINATION 521
The instantaneous ratio of CO2 assimilation rate of a leaf, A, to its
transpiration rate, E, is given approximately by
where ~, is the water vapor pressure difference between the intercellular spaces
and the atmosphere. The factor 1.6 arises because the binary diffusivity of
water vapor and air is 1.6-fold greater than that of COz and air. Equation 16
may be rewritten as
A 17.
E 1.6~, ’
to emphasize that a smaller value ofpi/p,~ is equivalent to an increase in A/E,
for a constant water vapor pressure difference, u. Thus selecting for lower
Pi/P,~ should be, to a first approximation, a screen for greater A/E, which, in
turn, is a component of transpiration efficiency. From Equation 8, A may be
used as a surrogate measure of Pi/P,, in Ca plants.
In all of the experiments relating gas exchange properties and short- and
long-term discrimination (see the section above on C3 photosynthesis) and
where vapor pressure difference, u, was maintained constant, the ratio of
assimilation and transpiration rates, A/E, was negatively related to A, as
expected from Equation 17. However, during whole-plant growth, losses of
carbon and water occur that are not included in Equation 17. A proportion,
~bc, of the carbon fixed via the stomata during the day is lost from the shoot at
night or from nonphotosynthetic organs such as the roots, during both the day
and night. Further, some water is lost from the plant independently of CO2
uptake. The stomata may not be completely closed at night, cuticular water
loss occurs, and there is unavoidable evaporative loss from the pots in
whole-plant experiments. If this "unproductive" water loss is a proportion,
4’w, of "productive" water loss, Equation 17 may be modified to describe the
molar ratio, W, of carbon gain by a plant to water loss
p,~(l- Pi](1-~b¢)p,,/
W = , 18.
1.6~’(1 + ~w)
which, when combined with Equation 8, predicts a negative linear depen-
dence of W on A (38, 60). By substitution, Equation 18 can be rewritten
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522 FARQUHAR ET AL
- a - a)(1 _ (kc)
Pa b - a
W= 19.1.6v(1 + (k,~)
where d is a correction related to assimilation rate (see Part III of the
Appendix). The data from pot experiments using a combination of watering
treatments and genotypes fit the theory reasonably well for a number of
species--wheat (39, 84), peanuts (61, 62, 162), cotton (59), tomato (83),
barley (60). We suggest that future studies will provide better understanding
of the relationships between W and A when account is taken of environmental
and genetic effects on (kc and (kw.
Scaling from the Plant to the Canopy
Water-use efficiency is difficult to measure in the field. There have, however,
been a few attempts to .relate it to A, or at least to relate yield under
water-limited conditions to A. Wright et al (162) measured total above-ground
biornass yield and water use of eight peanut genotypes receiving adequate
water (under a rain-excluding shelter). They obtained a negative relationship
between W and leaf A.
There are several reasons why the negative relationship between W and A,
given by Equation 19, might work well for individual plants in pots, or even
for small plots in the field, but become inconsistent over larger areas. The
uncontrolled loss of water is not an independent, fixed proportion ((kw)
transpiration because, for example, soil evaporation tends to be negatively
related to leaf area development. If v fluctuates, then those genotypes that
might grow more when v is small will obtain a greater W for the same A.
Equation 19 also contains a simplification that becomes more problematic
with increase of scale. The equation is written as if the vapor pressure
difference, v, were an independent variable. To some extent, however, it
must vary as stomatal conductance, gs, changes (as is the case for a single
leaf). A reduction in gs, and therefore in E, means more heat has to be lost by
sensible heat transfer. The- presence of a leaf boundary layer resistance to the
transfer of heat translates this into an increase of leaf temperature and of ~ and
so the effect of decreased gs on E is moderated. This moderating effect
increases as the ratio of boundary layer resistance to stomatal resistance
increases. With a sufficiently high ratio, the proportional reduction in E
caused by partial stomatal closure is no greater than the associated pro-
portional reduction in A. Farquhar et al (36) discussed the above problems and
defined the conditions that would be necessary for A/E to become independent
of stomatal conductance, Pi/Pa and A.
The problem is exacerbated in the field, where the aerodynamic resistance
of the crop has to be taken into account. If the canopy and leaf boundary layer
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CARBON ISOTOPE DISCRIMINATION 523
resistances to heat are very large, there is the possibility that a genotype with a
greater stomatal conductance than another otherwise identical genotype will
have a greater value of W (15), despite also having a greater A (36). This
more likely to occur at high temperatures. On the other hand, it is less likely
to occur when crops have very small leaf area indexes, as would normally be
the case under conditions where stress occurs early, and in crops sown in
areas prone to severe, early water stress, because under these conditions the
crop is more closely "coupled" to the atmosphere, like an isolated plant (15,
66). If the source of variation in A is the capacity for photosynthesis, the
effects of boundary layers are unimportant (15). This appears to be the case
for peanuts (62). Therefore at the crop level, identification of the causes
underlying differences in A may become important-~differences in con-
ductance having different micrometeorological consequences from dif-
ferences in photosynthetic capacity.
Carbon Isotope Discrimination and Plant Growth
Characteristics
Hubick et al (62) found a negative relationship between dry matter production
and A of peanut cultivars grown in field trials. On the other hand Condon et al
(14) saw a positive relationship between yield and/X for wheat cultivars in two
years that included periods of greater than usual rainfall. The sign of the
relatiotlship under well-watered conditions is difficult to predict. It is clear
that any associations between A and patterns of carbon partitioning will be
important. The relative growth rate, r (sec’l), of a plant depends on the
assimilation rate per unit leaf area, A (mol C -2 sec-~), and the ratio of t otal
plant carbon to leaf area, p (mol C m-2), according to the following identity
(84)
IA(1 - ~b~)
r = , 20.
P
where l is the photoperiod as a proportion of a day. Masle & Passioura (85)
observed that wheat seedlings grew more slowly in soil of increased strength
than in controls. Masle & Farquhar (84) showed that 19 increased with
increasing soil strength. They also found that A decreased with increasing soil
strength. Changing soil strength thus induced a negative relationship between
p and A. They noted that a similar, negative, but genetic association between
p and A would tend to cause a positive relationship between growth rate and
A. A negative association between 19 and A has been observed among wheat
and sunflower genotypes during early growth (J. Virgona, personal com-
munication). If v is low early in the life of a crop, then a positive association
between A and relative growth rate among genotypes will confound the
relationship between final W and A.
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524 FARQUHAR ET AL
Genetic Control of Discrimination
Genetic studies of W, Pi/p~, and A are in their infancy. These traits are most
likely to be polygenic, since any gene that affects either assimilation rate per
unit leaf area or stomatal conductance can have an effect. Despite the con-
siderable genetic and environmental (nutrition, light intensity, etc) effects
the individual components A and g, separately, it is likely that the variation in
the ratio A/g, and hence in pi/p~ and A, is smaller, because of coordination
between A and g (37). The coordination can lead to predictable genotypic
differences in P~/Pa and A as assessed from gas exchange (62), as well as in A
assessed from 6p.
The genetic control of A appears to be strong in wheat. Condon et al (14)
showed that genotypic ranking was maintained at different sites and between
plants grown in pots and in the field. The broad sense heritabilities [propor-
tion of total variance of A that can be ascribed to genotype, rather than to
environment or to interactions between the two (G × E)] ranged between
and 90%. From analyses of A in 16 peanut genotypes grown at 10 sites in
Queensland, Hubick et al (62) calculated an overall broad sense heritability
81%. With Phaseolus vulgaris in Colombia, it was 71% (23). Hubick et
(62; and see earlier discussion in reference 36) examined the progeny of
cross between Tifton 8, a peanut genotype having a small value of A, and
Chico, which has a large value of A. Statistical analyses of measurements of
A and W in the F2 generation gave estimates for the heritability of 53% for A
and 34% for W, The phenotypic correlation between W and A was --0.78. As
expected, the A values of F2 plants were highly variable and there were
several transgressive segregants with values of A lower than those of Tifton 8.
The A values of the F~ generation of the Tifton 8 and Chico cross, while
somewhat intermediate between the two parents, were very close to those of
Tifton 8 in A and W. Martin & Thorstenson (83) examined the F~ plants from
a cross between Lycopersicon pennellii, a drought-tolerant species related to
tomato, with tomato itself, Lycopersicon esculenturn. L. pennellii had a lower
A than L. esculentum, and again A of the F1 was intermediate, but closer to
the low-A parent. Both sets of data suggest some dominance of the low-A
attribute.
Genetic analysis of a polygenic trait like A is obviously difficult, yet
considerable progress has recently been made using modem techniques.
Martin et al (82) reported that 70% of the variance for A in a variable tomato
population derived from further generations of the above cross was associated
with three restriction fragment length polymorphisms (RFLPs)~i.e. genetic
markers identifying discrete DNA sequences within the genome. Additive
gene action was observed in the three cases, and in one of them, there was
also a significant nonadditive component. This kind of work may enable
breeders to follow the results of backcrossing material with desirable A into
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CARBON ISOTOPE DISCRIMINATION 525
commercial cultivars. However, in parallel with pursuing research on the
genetic control of carbon isotope discrimination by the plant, it is important to
establish what values of A are appropriate in a particular environment and for
a particular species. This requires extensive physiological work at different
scales, from the organelle to the canopy, and a much better understanding of
the interactions among plants, canopies, and their microclimates.
CONCLUDING REMARKS
Carbon isotope discrimination has become a tool to help us understand
photosynthesis and its coordination with water use in ecological and physi-
ological studies of C3 species. Future work will relate these more to growth
characteristics and will differentiate between effects of photosynthetic capac-
ity and stomatal conductance. The latter may perhaps be studied using
observations of isotopic composition of organic oxygen and hydrogen (36).
These compositions are affected by the ratio of ambient and intercellular
humidities and should therefore reflect changes in the energy budgets of
leaves, which are themselves influenced by stomatal conductance.
It is possible that measurements of A in C4 species may aid in seeking
changes in coordination between mesophyll and bundle sheath tissue during
photosynthesis, perhaps revealing differences in quantum requirements.
Technological advances in combining gas chromatography and isotope
ratio mass spectrometry should facilitate measurements of carbon isotope
discrimination between and within organic compounds, thereby increasing
our ability to identify origins of materials and to study the nature of the control
of metabolic pathways following photosynthesis.
ACKNOWLEDGMENTS
We thank Drs. Joe Berry and Josette Masle for valuable discussions and
comments on this manuscript.
APPENDIX
Part 1. Definitions Isotope effects (c~) are here defined as the ratio of carbon
isotope ratios in reactant and product (39)
A1.
where R~ is the 13C/12C molar ratio of reactant and Rp is that of the product.
in a first order kinetic reaction, the definition is obvious, i.e.
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526 FARQUHAR ET AL
k~2 A2.
where k~2 and k~3 are the rate constants for reactions of the respective isotopic
substances. Higher-order kinetic reactions including Michaelis-Menten ones
(38) can be treated similarly (102), and ~2 and k13 become pseudo-first-order
rate constants. The isotope effect associated with diffusion is the ratio of the
~2C and ~3C diffusivities. The analogy with Equation AI is the diffusion from
a source (reactant) to a sink where the "product" is kept at a vanishingly small
concentration. In an equilibrium, the "product" is the carbon-containing
compound of interest on the right-hand side of an equilibrium reaction. So if
the reaction of interest is
kl
A ~B, A3.
k_~
where A and B might be COz and HCO~-, for example, then application of this
rule yields
A~3
Al~ Kl2
-- A4.¢~ = B13
K13 ,
where K~2 is the equilibrium constant,
A5.
for the ~2C compounds and K~3 is the analogous constant for 13C compounds.
Note that the equilibrium isotope effect, ~x, is the kinetic isotope effect for the
forward reaction (a0 divided by that of the reverse reaction (c~_~---i.e.
It is pleasing then that the forms of the isotope effect (t~) for kinetic effects
(k~2/k13) and equilibrium effects (KtZ/K13) are superficially similar. We de-
note the discrimination for either effect as ct minus one (39). In most cases
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CARBON ISOTOPE DISCRIMINATION 527
discrimination associated with a kinetic effect will be positive, but there is no
a priori reason why a thermodynamic discrimination should be positive.
Part 1I. Discrimination in a simple two stage model---diffusion followed by
carboxylation The carbon isotope ratio of CO2 in air is R~, and in the plant
product is Re. In turn Rp must be the same as the ratio of ~3CO2 assimilation
rate, A13, and ~2CO2 assimilation rate, A [no superscript is given here for a
variable relating to the major isotope ~2C]--i.e.
A13
Re = A A7.
Further, if the isotope effect associated with carboxylation is 1 + b, then we
must have
gi
--=l+b, A8.
where Ri is the carbon isotope ratio of the intercellular C02.
In turn, Ri is simply found by relating A to g (conductance) and P (total
pressure). Thus,
A = g(P" - Pl) A9.
P
The kinetic isotope effect for diffusion is the ratio of the diffusivities of lZCO2
and ~3CO2 in air. Thus,
1 + a = ~g AI0.
g13 ’
and so
AI 3 = g(Rap~ - Ripl)(1 + a)P
Substituting Equations A9 and A11 in A7,
Rap,~ - Ripi
All.
(1 + a)(pa -Pi)"
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528 FARQUHAR ET AL
Rearranging,
R~ Pa - Pi Ri Pi
--=(1 +a)
Thus, using the definition of discrimination and Equation A8
a 1 + A Ro (1 + a) p° - pi + (1 + b) pi
Rp Pa Pa
Thus
A = a Pa -- Pi + b P__L,
Pa Pa
which is Equation 8 from the main text. Note that no assumption of linearity is
made about the response of A to p~ in the derivation of this equation.
Part 1II. Alternative definitions of discrimination There are other possible
definitions of discrimination. For example one could write
Discrimination* = 1 - --
This would correspond to (1 - kl3/k 12) for kinetic effects and to (1
Kla/K12) for equilibrium effects. The asterisk superscript is added to empha-
size that the numerical values obtained differ from those made using Equation
4. On this basis
The numerical differences between this and our chosen definition of dis-
crimination are usually less than 0.5%0. In the case of discrimination by
ribulose bisphosphate carboxylase (Rubisco), the two definitions differ by
0.9%0, which is significant. However, formulation of discrimination as A*
rather than as (Ra/Rt, - 1), would make derivation of the theory much more
complicated. This may be seen by repeating the derivation in Part II ,using a*
= 1 - gl3/g and b* = 1 - Rp/Ri.
Although it may seem odd to have the abundance ratio of the source, Ra, in
the numerator of our chosen definition (Equation A1), we note that RdR~ may
equally be thought of as SplSa, where S is the molar ratio 12C/13C.
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CARBON ISOTOPE DISCRIMINATION 529
Yet another notation is to use Rp/R~ - 1, kl3/k 12 - 1, and K13/K12 - I,
which leads to negative values of discrimination.
Part IV. Complications to the use of A = a + (b - a)pi/Pa Farquhar (34)
showed that the appropriate value of Pi in Equation 8 is the assimilation-rate-
weighted value of pi, whereas normal gas exchange gives a conductance-
weighted value of p;. These two estimates will differ if there is heterogeneity
of stomatal opening (73, 141) and restricted lateral diffusion within the leaf.
Greater degrees of heterogeneity will therefore cause smaller best fit values
for b. The simplest value of b would be the isotope discrimination factor of
Rubisco carboxylation, taking gaseous COz as the substrate (b3). Roeske
O’Leary (119) measured the isotope effect as 1.029, but with respect
dissolved CO2, so that the result must be multiplied by the isotope effect of
the dissolution of CO2 in water (1.0011) making b3 approximately 30%0 (36).
Guy et al (50) measured the effect directly with respect to the gas
monitoring continuing isotopic enrichment of CO2 in a reaction vessel and
calculated b3 to be -- 29%0 using an equation analogous to that for Rayleigh
distillation (7, 97). However, Farquhar & Richards (39) suggested that the
discrimination in Ca photosynthesis should be less than that in the Rubisco
carboxylation, because even in Ca species a portion,/3, of COz fixation is via
PEP carboxylase. With b4 being the net fractionation by PEP carboxylase
with respect to gaseous CO2 in equilibrium with HCO~, (-5.7%0; see Table
1) they suggested a net discrimination value of
b = (l-~)b3 + Bb4 = b3 - ~(b~ - b4).
The difference (b3 - b4) is - 36%0, so that b is sensitive to the proportion of
/3-carboxylation. The latter depends on the amount of aspartate to be
formed~unlikely to vary much between plants--and the amount of HCO~-
formed for pH balance. This latter factor may contribute to the greater
discrimination shown by Ricinus plants grown with NH~- as N source than
when NO~- was the sole source, although the phenomenon was interpreted in
terms of changed stomatal behavior (114). In an unpublished study by Melzer
& O’Leary (personal communication), Ca fixation was found to reduce
carbon discrimination by no more than 1%o in C3 species. Assuming Pi/Pa was
~ 0.7, this means that b could be reduced from b3 by 1.9%o.
Other effects are ignored in the simple model represented by Equation 8.
These include the presence of resistance between the intercellular spaces and
the sites of carboxylation, and effects of respiratory losses and translocation.
Many of these effects are taken into account in a more detailed equation (32)
for which Equation 8 is a simplification:
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530 FARQUHAR ET AL
eR__~ + fF*
P. - Ps Ps - Pi Pi - P~ Pc kA = ab --+ a~ + (es + a])~+ ,A12.
Pa Pa Pa Pa Pa
where ps is the p(CO2) at the leaf surface, pc is the equivalent p(CO2) at the
sites of carboxylation, ab is the fractionation occurring during diffusion in the
boundary layer (2.9%o), es is the fractionation occurring as CO2 enters
solution [1.1%o at 25°C; (149)] at is the fractionation due to diffusion in water
[0.7%0; (98)], e and f are fractionations with respect to average carbon
composition associated with "dark" respiration (Rd) and photorespiration,
respectively, k is the carboxylation efficiency, and F* is the CO2 compensa-
tion point in the absence of Rd (32).
Equation 8 overestimates discrimination compared to Equation A12 by
d = [rb(a -- ab) + rw(b - es - at)] AP +
Pa
eed
Pa
A13.
The resistances rb and rw (mz sec tool 1) are those of the boundary layer, and
between the intercellular spaces and the sites of carboxylation, respectively,
and P is the atmospheric pressure. Thus Equation 8 should overestimate
discrimination at a fixed Pi/Pa by an amount (d) that increases with increasing
assimilation rate, as may tend to occur naturally with increasing light intensity
(32).
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