Download on the potential efficiency of converting solar radiation to phytoenergy

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From sunlight to phytomass: on the
potential efficiency of converting solar
radiation to phyto-energy
Author for correspondence:
Jeffrey S. Amthor
Tel: +61 02 8627 1050
Email: [email protected]
Jeffrey S. Amthor
Faculty of Agriculture, Food and Natural Resources (C81), University of Sydney, NSW 2006,
Australia
Received: 10 July 2010
Accepted: 5 September 2010
Contents
Summary
939
VII. Maintenance
949
I.
Introduction
940
VIII. Substrate requirement for growth
949
II.
Approach
940
IX.
From sunlight to phyto-energy: potential overall efficiency 953
III.
Solar radiation absorption
942
X.
Assessment
955
IV. Quantum requirement for CO2 assimilation
943
Acknowledgements
955
V.
946
References
955
Respiration
VI. Photosynthate mobilization and translocation
948
Summary
New Phytologist (2010) 188: 939–959
doi: 10.1111/j.1469-8137.2010.03505.x
Key words: C3 ⁄ C4, efficiency, growth, maintenance, photorespiration, photosynthesis,
respiration, solar radiation.
The relationship between solar radiation capture and potential plant growth is of
theoretical and practical importance. The key processes constraining the transduction of solar radiation into phyto-energy (i.e. free energy in phytomass) were
reviewed to estimate potential solar-energy-use efficiency. Specifically, the output : input stoichiometries of photosynthesis and photorespiration in C3 and C4
systems, mobilization and translocation of photosynthate, and biosynthesis of
major plant biochemical constituents were evaluated. The maintenance requirement, an area of important uncertainty, was also considered. For a hypothetical C3
grain crop with a full canopy at 30C and 350 ppm atmospheric [CO2], theoretically potential efficiencies (based on extant plant metabolic reactions and
pathways) were estimated at c. 0.041 J J)1 incident total solar radiation, and
c. 0.092 J J)1 absorbed photosynthetically active radiation (PAR). At 20C, the
The concept for this article was developed
while the author was employed by the US
Department of Energy; it does not reflect
any US Government view or policy.
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calculated potential efficiencies increased to 0.053 and 0.118 J J)1 (incident total
radiation and absorbed PAR, respectively). Estimates for a hypothetical C4 cereal
were c. 0.051 and c. 0.114 J J)1, respectively. These values, which cannot be considered as precise, are less than some previous estimates, and the reasons for the
differences are considered. Field-based data indicate that exceptional crops may
attain a significant fraction of potential efficiency.
I. Introduction
How much plant can be grown from a unit input of solar
radiation? This question, which has broad theoretical and
practical implications, has been addressed previously (e.g.
Loomis & Williams, 1963; Beadle & Long, 1985; Loomis
& Amthor, 1996, 1999; Long et al., 2006; Zhu et al.,
2008), but remains incompletely resolved. The goal of this
review is to synthesize the present knowledge about the
process stoichiometries underlying the transduction of solar
radiation into phyto-energy (i.e. free energy contained in
phytomass) to arrive at an estimate of the potential (theoretically maximal) efficiency of whole-plant productivity. It
focuses on extant plant properties (e.g. C3 plants with photorespiration), but the analysis is expected to contribute to
an understanding of how genetic modifications might
increase plant production (Reynolds et al., 2000; Murchie
et al., 2009; Zhu et al., 2010).
The relationship between solar radiation input and plant
production (or output) is often expressed as the phytomass
grown per unit of solar radiation intercepted or absorbed
(kg MJ)1). A more meaningful ratio is that of the accumulated phyto-energy per unit solar radiation input (J J)1),
because that is a true efficiency. Phyto-energy accumulation
is the change (during a defined period) in the product of
phytomass heat of combustion (DHC, MJ kg)1) and phytomass per unit ground area (kg m)2). Solar radiation input
(incident or absorbed) in MJ m)2 is integrated over the
same period. The ratio, or solar-energy-use efficiency,
circumvents the difficulties in comparing plants with different DHC. For example, grain sorghum (Sorghum bicolor)
whole-plant DHC was 17.2 MJ kg)1, whereas adjacently
grown soybean (Glycine max) contained 19.1 MJ kg)1
(Amthor et al., 1994). The 11% greater soybean DHC must
be considered when comparing solar energy use between
the species. Indeed, a wide range of DHC is found among
organs and species (Table 1) and, especially, among plant
biochemical constituents (Table 2). Differences among
organs harvested from different crop species can be noteworthy: values for potato (Solanum tuberosum) tubers,
wheat (Triticum aestivum) ears, maize (Zea mays) seeds,
lupin (Lupinus albus) pods, soybean pods and sunflower
(Helianthus annuus) seeds were 16.8, 17.3, 18.2, 19.1, 21.1
and 26.9 MJ kg)1, respectively (Shinano et al., 1993).
Unfortunately, DHC is infrequently measured in plant
production studies.
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The amount of phyto-energy accumulated depends on
the amount of solar energy captured and the efficiency of its
use (Loomis & Williams, 1963; Warren Wilson, 1967;
Monteith, 1972, 1977; Dohleman & Long, 2009). This
review targets the efficiency – specifically, potential (maximal) efficiency – of the conversion of solar energy to phytoenergy. Emphasis is placed on C3 and C4 grain crops
because of their importance to humans, the availability of
data and personal interest, but the approach is general.
II. Approach
Studies of potential (or actual) solar-energy-use efficiency
follow a general pattern (Fig. 1). The fate of a unit of solar
radiation incident on a plant community is traced through
a series of ‘processes’ or steps, ending with new phytomass
production. The ‘output : input’ ratio of each step is evaluated using physical or biochemical theory, a summary of
empirical observations, or both. Indeed, analyses of
potential efficiencies often rely on observations of actual
efficiencies when underlying theory is insufficiently developed.
This review considers each of the processes (steps) in
Fig. 1, and assigns or derives values the reviewer believes to
be appropriate to the potential efficiency for extant plants.
After briefly considering the spectral properties of solar radiation and how effectively plants can absorb it (the top ‘half’
of Fig. 1a,b), the analysis turns to quantitative biochemistry. This includes summing up the reactions that convert
CO2 to photosynthate (i.e. sucrose and starch) to quantify
the stoichiometries between CO2 assimilation and the input
of ATP and NADPH required from photochemistry.
Photosynthesis and photorespiration by C3 and C4 plants
are considered separately and compared. The metabolic cost
of photosynthate translocation is considered, and the
whole-plant maintenance energy requirement is estimated.
Reactions that convert the remaining photosynthate (i.e.
photosynthate remaining after translocation and maintenance energies are expended) to the main components of
new structural phytomass (cellulose, hemicelluloses, lignins,
proteins, lipids and organic acids) are summed to quantify
the stoichiometries between growth, ATP and NADPH use
(requirement), and photosynthate consumption.
The output : input ratio (J J)1) is the measure of efficiency applied to component processes. It is herein symbolized as YE and is estimated by dividing the energy content
of end products by the energy content of substrate inputs,
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Table 1 Selected measured phytomass heats of combustion
Heat of combustion (DHC, MJ kg)1)
Species
Root
Stem, wood
Leaf
Seed, fruit
Whole plant
Source
Glycine max
Helianthus annuus
18.3
16.5
19.3
16.5
16.7
13.4
17.0
17.2
16.1
16.8
18.2
17.5
17.4
17.7
17.7–20.4
20.2
17.7
17.6
19.0
16.0
14.2
19.0
17.7
16.9
19.0
18.8–21.0
22.0
17.5
16.1
22.8
28.3
21.0
19.1
16.7
18.1
18.0
17.2
17.5
A
B
C
D
A
C
E
F
B, F
G
G
Miscanthus · giganteus
Sorghum bicolor
Zea mays
Juglans regia (seedlings)
Hardwood forest trees
Pinus species
Tropical mangrove forest
Tropical moist forest
16.9
16.6
17.0
18.0
33.3
23.5–29.8
17.0
18.0
Glycine max ‘root’ included nodules.
Sources: A, Amthor et al. (1994); B, Long (1934); C, Lieth (1968); D, Beale & Long (1995); E, Gary et al. (1995); F, Gower et al. (1984);
G, Golley (1969).
Table 2 Heats of combustion of key phytomass constituents
Fraction carbon
Heat of combustion (DHC)
Constituent
(kg C kg)1)
(MJ kg)1)
[MJ
(mol C))1]
Fructose
Glucose
Sucrose
Starch
Cellulose
Hemicelluloses1
Lignins2
Amino acids3
Lipids4
Organic acids5
0.4000
0.4000
0.4211
0.4444
0.4444
0.409–0.493
0.631–0.725
0.297–0.654
0.666–0.776
0.267–0.414
15.60
15.57
16.49
17.48
17.35
13.39–20.95
26.24–30.50
13.91–31.62
33.28–39.69
2.70–11.41
0.4684
0.4675
0.4703
0.4725
0.4687
0.393–0.510
0.500–0.507
0.400–0.750
0.600–0.627
0.122–0.332
Details are given in Supporting Information Table S1.
1
, Ranges for arabinose, xylose, fucose, galactose, glucuronate,
methylated glucuronate, mannose and rhamnose residues in
hemicelluloses.
2
, Ranges for p-coumaryl alcohol, coniferyl alcohol and sinapyl
alcohol residues in lignins.
3
, Ranges for the 20 amino acid residues in proteins.
4
, Ranges for capric acid, caprylic acid, glyceryl trioleate, glyceryl
tripalmitate, lauric acid, linoleic acid, linolenic acid, myristic acid,
oleic acid, palmitic acid and stearic acid.
5
, Ranges for aconitic acid, citric acid, malic acid, oxalic acid and
oxaloacetic acid (OAA).
including solar radiation. A new compilation of plant constituent DHC values is used to evaluate YE of metabolism.
Because the pathways of anabolic and catabolic carbon
flow are well understood, the related potential stoichiometries can be quantified mechanistically. Quantitative relationships between photon absorption and photosynthetic
NADPH formation, and between carbohydrate oxidation
and respiratory NAD(P)H production, are also established
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mechanistically. Conversely, stoichiometries of photon
absorption and photophosphorylation, mitochondrial electron transport and oxidative phosphorylation, energetics of
translocation and maintenance requirement are debated or
unresolved.
After the potential efficiencies of each process (step) have
been evaluated, they are multiplied together to obtain the
overall potential efficiency of conversion of solar radiation
to phyto-energy (see Monteith, 1972). The overall potential
efficiency is compared with results from similar theoretical
studies, and with field measurement-based estimates of
actual efficiencies of exceptional plant communities.
This review acknowledges that sucrose and starch are the
main products of photosynthesis (Heldt, 2005), and that
sucrose is the main (not sole) form of carbon translocated
throughout plants (Ziegler, 1975; Lunn & Furbank, 1999;
Rennie & Turgeon, 2009; Slewinski & Braun, 2010). In
this analysis, respiration and growth are initiated by cleaving
sucrose with invertase (yielding glucose and fructose) or
sucrose synthase (yielding fructose and UDP-glucose), as
considered appropriate for specific processes. Historically,
glucose was specified as the product of photosynthesis and
the initial substrate of growth and respiration (Penning de
Vries et al., 1974; Williams et al., 1987; Thornley &
Johnson, 1990). For plant growth and respiration, this was
a hold over from studies of micro-organisms that resulted
in minor differences in the calculated potential process
efficiencies relative to sucrose-based plant metabolism
(examples below).
Importantly, all analyses of potential solar-energy-use
efficiency reduce complex (bio)physical and (bio)chemical
processes to simplified summaries. The goal is to encapsulate the overriding quantitative relationships in these
summaries to provide a useful and realistic (not necessarily
precise) model of reality.
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Tansley review
Potential (maximal) efficiency
100
Total solar radiation (incident)
55.6
Not photosynthetically active (incident)
3.7
Canopy albedo
4.44
Inactive absorption
44.4
Photosynthetically active (incident)
40.7
Absorbed by leaves
36.26
Absorbed by photosynthetic pigments
28.34 Lost as heat (and fluorescence)
7.92
Assimilated in photosynthesis
1.98
5.94
(b)
New free energy in phytomass
Actual (observed) efficiency
100
Total solar radiation (incident)
55
Not photosynthetically active (incident)
7
Canopy albedo
3
Inactive absorption
31
Lost as heat (and fluorescence)
1.0
Maintenance respiration
0.8
Growth respiration
45
Photosynthetically active (incident)
38
Absorbed by leaves
35
Absorbed by photosynthetic pigments
4.0
Assimilated in photosynthesis
3.0
2.2
Respiration
Available for growth
New free energy in phytomass
Fig. 1 Two classic analyses of solar-energy-use efficiency for
phytomass production: (a) potential (theoretically maximal)
efficiency adapted from Loomis & Williams (1963) and (b)
generalized actual efficiency adapted from Warren Wilson (1967).
For both analyses, plant communities intercept all incident solar
radiation and the 400–700 nm waveband is designated as
photosynthetically active radiation (PAR). Numerical values indicate
relative energy units. Bold text and arrows indicate ‘retention’ of
solar energy; others indicate energy losses. Potential efficiency was
based on 4.65 mol photons MJ)1 PAR and a 10-photon
requirement to assimilate a CO2 molecule; the analysis was
conducted before full appreciation of the photorespiration and
metabolic differences between C3 and C4 plants. As adapted here,
the potential efficiency is 12% greater than the result given by
Loomis & Williams (1963) to account for the 12% greater energy
concentration (DHC) in ash-free phytomass compared with
photosynthate; that is, some of the energy in the respiratory
substrate of Loomis & Williams (1963) is herein retained in new
phytomass. As adapted here, based on the data summarized by
Warren Wilson (1967), actual efficiency involves a ‘true growth
yield’ of 0.73, rather than the value of 0.67 used in the original
analysis.
III. Solar radiation absorption
The 400–700 nm waveband is usually designated ‘photosynthetically active radiation’ (PAR) (McCree, 1981).
Equating PAR with this waveband sparked modest controversy several decades ago, but it is now generally accepted
without question. Only c. 39% of extraterrestrial solar
energy is in the 400–700 nm waveband (Gueymard, 2004),
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but this fraction increases as solar radiation approaches
Earth’s surface because the atmosphere more strongly
absorbs and reflects radiation outside this waveband. The
fraction at Earth’s surface varies with location, season, solar
elevation and sky condition, topics beyond present consideration (see, for example, Monteith, 1972). Based on
summer data in a comprehensive study at 36.6N latitude
(Texas, USA), 48% is taken as a representative fraction of
total solar energy that is in the 400–700 nm waveband
(Britton & Dodd, 1976).
Because photosynthesis is a quantum process, the distinction between solar energy flux (irradiance) and photon flux
density is important; photon energy is inversely related to
wavelength, so that the potential efficiency of energy use is
greater with longer wavelength photons. The maximal spectral solar irradiance may occur at c. 450–500 nm, whereas
the maximal spectral photon flux density occurs more
broadly and at longer wavelengths (e.g. c. 550–700 nm)
(Fig. 2a,b). In leaves, low-light CO2 uptake per absorbed
photon is greater in the 550–675 nm waveband than in the
425–550 nm waveband (Fig. 2c), and photosynthesis can
be driven by photons outside the 400–700 nm waveband
(although the ‘spillover’ is modest; Fig. 2c), and so there is
no simple (square-wave) spectral gauge of PAR (and see
Evans, 1987). Nonetheless, photons with wavelengths
beyond c. 700 nm are insignificant for oxygenic photosynthesis (Emerson, 1958; Ort & Yocum, 1996), leaf absorptance declines sharply between 700 and 750 nm (McCree,
1972a) and the fraction of solar energy with wavelengths
< 400 nm is small (Fig. 2), and so the 400–700 nm waveband is a reasonable definition of PAR. McCree (1972b)
suggested that clear-sky (sun plus sky) PAR contained
4.57 mol photons MJ)1, which is the value adopted herein
(the illustrative spectra in Fig. 2a,b yield the ratio 4.55).
The fraction of incident solar radiation intercepted by a
plant community depends on the leaf area and orientation.
Sparse canopies intercept little radiation; dense canopies
may intercept it all. Intercepted radiation is absorbed, transmitted or reflected. Canopies fully intercepting incident
solar radiation might absorb 90–95% of PAR in the solar
spectrum (e.g. Hipps et al., 1983). However, some of that
PAR may be absorbed by pigments that do not contribute
to photosynthesis, and so an allowance was made for
inactive PAR absorption by Loomis & Williams (1963).
Speculative values for inactive absorption of c. 4–10% of
intercepted PAR have been given (Loomis & Williams,
1963; Warren Wilson, 1967; Long et al., 2006). The 10%
value used by Loomis & Williams (1963) was based on
leaf-level data; a canopy-scale value might differ. The issue
of inactive absorption, especially at the canopy scale, is
unresolved and sometimes ignored. For present purposes, it
is assumed that a full canopy can absorb 93% of incident
PAR and that 92% of that absorption can be by photosynthetic pigments.
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1. C3 photosynthesis
Spectral irradiance
(J m–2 s–1 nm–1)
(a)
1.5
C3 photosynthesis – from CO2 to fructose 6-P – can be
summarized by (Supporting Information Table S2a):
1.0
0.5
6 CO2 þ 18 ATP þ 12 NADPH
! fructose 6-P þ 18 ADP þ 17 Pi þ 12 NADP:
0
Spectral photon flux
(µmol m–2 s–1 nm–1)
(b)
6
4
2
0
(c)
Relative CO2 uptake
(CO2/absorbed photon)
Review
1.0
0.5
0
300
400
500
600
700
Wavelength (nm)
800
900
1000
Fig. 2 (a) Spectral horizontal solar irradiance, 5 m above green
grass, at Lincoln, Nebraska (USA), at 11:30 h local time (c. 10:58 h
solar time) on 10 August 2010, simulated with SMARTS version
2.9.5 (Gueymard, 1995, 2001, 2004) for a clear sky (calculated
atmospheric transmittance of c. 0.73). Calculations covered the
waveband 280–4000 nm, but only results for 290–1000 nm are
shown. This simulation is for illustrative purposes; the actual
irradiance at any time and place may depart from these values
because of differences in time ⁄ date, location and sky conditions, but
the relative spectral distribution represents general daylight well. (b)
Spectral photon flux area density corresponding to irradiance in (a),
with the 400–700 nm waveband hatched. (c) Relative ‘spectral
photosynthesis’ of leaves of eight field-grown plant species (i.e. net
CO2 assimilated, adjusted for respiration rate in the dark at the same
temperature) per absorbed photon, scaled to a maximum value of
1.0 (McCree, 1972a; and see McCree, 1981). The eight-species
mean is shown by the wide continuous (central) line; narrow
continuous lines show minimal and maximal values among the eight
species. The dashed line indicates a laboratory-grown Brassica
oleracea leaf after removal of the adaxial epidermis (McCree &
Keener, 1974); the optical properties of the epidermis reduce the
use of photons with wavelengths below c. 400 nm for
photosynthesis. In (a), there are 411 J m)2 s)1 in the 400–700 nm
waveband and, in (b), there are 1872 lmol (photons) m)2 s)1 in
this waveband, which results in 4.55 mol photons MJ)1 between
400 and 700 nm.
IV. Quantum requirement for CO2 assimilation
The quantum requirement is the number of photons that
must be absorbed to assimilate a CO2 molecule
(photon ⁄ CO2). It depends on ATP and NADPH requirements for CO2 assimilation, and the number of photons
needed to generate this ATP and NADPH.
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Thus, the photosynthesis of fructose 6-P requires three
ATP and two NADPH molecules per CO2 molecule but,
to drive photosynthesis to completion, that is to sucrose or
starch, an additional 1 ⁄ 12 or 2 ⁄ 12 ATP ⁄ CO2 is required,
respectively (Table S2b,c). The ATP and NADPH required
for photosynthesis can result from photosynthetic linear
(whole-chain) electron transport (LET) coupled to photophosphorylation, possibly in combination with cyclic electron transport (CET) and ⁄ or pseudocyclic electron
transport, also coupled to photophosphorylation (Asada,
1999; Allen, 2003; Yin et al., 2004).
For LET, four photons absorbed by pigments associated
with photosystem II (PS II) are sufficient to extract four
electrons from two water molecules and to release one O2
molecule and four protons into the chloroplast thylakoid
lumen. The electrons are transported to plastoquinone (Q)
within the thylakoid membrane, forming reduced plastoquinone (QH2). Cytochrome b6f, in turn, transports
electrons from QH2 to photosystem I (PS I) via plastocyanin (PC). Electron transport from PS II to PS I is coupled
to the translocation of protons from the chloroplast stroma,
through the thylakoid membrane, into the thylakoid lumen.
If a ‘Q-cycle’ of Q reduction ⁄ oxidation is engaged, which
may be likely under physiological conditions (Berry &
Rumberg, 1999; Sacksteder et al., 2000), two protons are
translocated per electron transported (i.e. H+ ⁄ e) = 2).
Without a Q-cycle, H+ ⁄ e) = 1.
The absorption of another four photons, by PS I pigments, can drive the transport of four electrons from PS I to
ferredoxin (Fd) and then to Fd-NADP reductase, reducing
two NADP molecules in the chloroplast stroma. [One electron reduces one Fd and two reduced ferredoxin (Fdred)
reduce one NADP.] In sum, the absorption of eight photons (four by PS I, four by PS II) can reduce two stromal
NADP molecules – meeting the NADPH requirements to
assimilate one CO2 molecule – and deposit up to 12 protons in the thylakoid lumen.
Protons moving from the lumen into the stroma, via
CF1–CF0 ATP synthase complexes traversing thylakoid
membranes, drive photophosphorylation. The number of
protons passing through an ATP synthase per ADP phosphorylated (H+ ⁄ ATP) places a limit on ATP production.
For some time, H+ ⁄ ATP was thought to be about three,
based on in vitro measurements, but more recent experimental results give about four (e.g. Van Walraven et al.,
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1996; Turina et al., 2003; Steigmiller et al., 2008). At
about the same time, the number of c subunits in the CF0
rotor ring was found to be 14 (Seelert et al., 2000; Vollmar
et al., 2009), which may be critical, because this number
divided by the number of catalytic sites on CF1 (i.e. three)
might ‘mechanistically’ define H+ ⁄ ATP (von Ballmoos
et al., 2009). In this case, it is 14 ⁄ 3 (c. 4.67), 17% greater
than the ‘measured’ value of four. Consensus on in vivo
H+ ⁄ ATP does not yet exist, however (more below).
With H+ ⁄ ATP equal to either four or 14 ⁄ 3, eight photons depositing 12 protons into the lumen could generate
three or c. 2.57 ATP, respectively, neither sufficient to meet
the ATP demands given above to photosynthesize sucrose
or starch (but matching exactly the three ATP ⁄ CO2
required for photosynthesis of fructose 6-P if H+ ⁄ ATP is
four). The deficit (0.083–0.595 ATP ⁄ CO2) might be met
by cyclic photophosphorylation (involving CET) or pseudocyclic photophosphorylation; CET is considered herein
because it can produce more ATP per photon. For CET,
which involves only PS I without O2 production or NADP
reduction, up to two protons can be translocated into the
lumen per absorbed photon (involving a Q-cycle), so that
each photon might give rise to 0.50 or c. 0.429 ATP (for
H+ ⁄ ATP = 4 or 14 ⁄ 3, respectively). For C3 photosynthesis
producing sucrose, the quantum requirement would be c.
8.17 or c. 9.19 photon ⁄ CO2 with H+ ⁄ ATP = 4 or 14 ⁄ 3,
respectively. Hence, H+ ⁄ ATP has a marked effect on the
potential quantum requirement.
2. Photorespiration
Although ribulose-1,5-P2 carboxylase ⁄ oxygenase (rubisco)
initiates C3 photosynthesis by carboxylating ribulose1,5-P2, it also initiates photorespiration – one of the
Earth’s most active metabolic pathways – by oxygenating
ribulose-1,5-P2 (Bowes & Ogren, 1972; Lawlor, 2001).
Photorespiration constrains solar-energy-use efficiency, but
may benefit some plants by dissipating ‘excess’, potentially
damaging absorbed radiation in stressful circumstances
(Wingler et al., 2000; but also see Long et al., 2006).
The photorespiratory cycle can be summarized for one
ribulose-1,5-P2 oxygenation by (Table S3a):
10 ribulose1; 5-P2 þ 15 O2 þ 34 ATP þ 20 NADPH
! 9 ribulose 1; 5-P2 þ 5 CO2 þ 34 ADP þ 36 Pi þ 20 NADP
where only 10 of the ‘15 O2’ molecules oxygenate ribulose1,5-P2 (the other five O2 molecules oxygenate glycolate).
For each rubisco-catalyzed oxygenation, 0.5 CO2 is released
and 3.4 ATP plus two NADPH are used (i.e. one NADPH
and two Fdred, which is equivalent to two NADPH). The
absorption of eight photons driving LET can therefore meet
NADPH requirements for one oxygenation, but not the full
ATP need (as above for the photosynthesis of sucrose or
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starch). In this case, the deficit is 0.40–0.83 ATP per oxygenation. If cyclic photophosphorylation fills this deficit,
the theoretical photorespiratory quantum requirement (or
penalty) is 8.8 or c. 9.93 photons per oxygenation with
H+ ⁄ ATP = 4 or 14 ⁄ 3, respectively.
The introduction of a bacterial glycolate degradation
pathway into Arabidopsis thaliana (Kebeish et al., 2007) has
important implications for the photorespiratory quantum
penalty. Substitution of this pathway for the photorespiratory cycle can be summarized by (Table S3b):
10 ribulose1;5-P2 þ 10 O2 þ 29 ATP þ 15 NADPH þ 5 NAD
! 9 ribulose 1;5-P2 þ 5 CO2 þ 29 ADP þ 31 Pi þ 15 NADP þ 5 NADH
Relative to normal photorespiration, this reaction set requires
0.5 fewer ATP and 0.5 fewer NADPH per oxygenation.
Moreover, it produces 0.5 NADH per oxygenation. One CO2
is still released for every two oxygenations but, as implemented
in A. thaliana, the CO2 is released within the chloroplast
(rather than the mitochondrion as in normal photorespiration) which could modestly inhibit oxygenation. Further
calculations herein assume unmodified photorespiration.
3. Integrated C3 metabolism
The quantum requirement for net CO2 assimilation (photosynthesis minus photorespiration) in the absence of respiration (QR, photon ⁄ CO2) is a combination of the quantum
requirements for photosynthesis and photorespiration as
follows (Table S4):
QR = QR;S þ ðQR;C þ QR;O vO =vC Þ=ð1 0:5vO =vC Þ
where QR,S is the quantum requirement (photon ⁄ C) to convert fructose 6-P to photosynthetic end product (e.g.
sucrose or starch), QR,C is the quantum requirement for the
photosynthesis of fructose 6-P (photon ⁄ CO2), QR,O is the
quantum requirement for photorespiration (photon ⁄ oxygenation), vO ⁄ vC is the ratio of ribulose-1,5-P2 oxygenation
to carboxylation (O2 ⁄ CO2) and 0.5 is the CO2 released per
ribulose-1,5-P2 oxygenation (CO2 ⁄ O2).
In C3 plants, temperature and [CO2] affect vO ⁄ vC (which
is related to rubisco’s CO2 ⁄ O2 specificity, and may be species
specific) and therefore QR (Fig. 3). Hence, there is no single
theoretical C3 plant QR. With H+ ⁄ ATP = 14 ⁄ 3, vO ⁄ vC = 0.35
and photosynthesis producing sucrose, QR is c. 15.3 photons ⁄
CO2; if H+ ⁄ ATP = 4, however, QR is c. 13.6 photons ⁄ CO2
(Table 3). Remarkably, in C3 plants at 11C, changing
H+ ⁄ ATP from 4 to 14 ⁄ 3 is equivalent, with respect to QR, to
changing ambient [CO2] from 700 to 350 ppm (Fig. 3b).
4. C4 photosynthesis
For present purposes, C4 photosynthesis refers to the
NADP malic enzyme type, which includes the major C4
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1.0
Ratio vO/vC
(oxygenation/carboxylation)
270
Table 3 Theoretical (minimal) quantum requirements for CO2
assimilation in the absence of respiration
0.8
Quantum requirement
(photon ⁄ CO2)
350
0.6
0.4
700
System
vO ⁄ vC
C4 overcycling
H+ ⁄ ATP = 4
H+ ⁄ ATP = 14 ⁄ 3
C3
0.00
0.10
0.20
0.35
0.50
0.70
0.00
0.03
0.03
0.03
0.03
–
–
–
–
–
–
0.00
0.00
0.05
0.10
0.20
8.17
9.51
11.01
13.60
16.70
21.95
12.17
12.62
12.82
13.02
13.43
9.19
10.71
12.40
15.32
18.82
24.74
13.86
14.37
14.61
14.85
15.32
0.2
[CO2]
0
C4
Quantum requirement
(photon/CO2)
(b)
30
270
25
350
20
15
700
C4
10
5
0
10
C3 minimum
20
30
Leaf temperature (°C)
40
Fig. 3 (a) Calculated C3 leaf vO ⁄ vC (the ratio of rubisco-catalyzed
ribulose-1,5-P2 oxygenations ⁄ carboxylations; see Farquhar & von
Caemmerer, 1982) as affected by temperature and ambient [CO2]
(ppm). The relationship vO ⁄ vC = 2C* ⁄ Ci is shown, where C* is the
CO2 photocompensation concentration (ppm) in the absence of
respiration and Ci is the intercellular [CO2]. Ci was taken to be
0.72 · ambient [CO2] for healthy C3 leaves, although the ratio
declines slightly with increased [CO2] (Long et al., 2004). C* was
calculated after Bernacchi et al. (2001):
C ¼ exp½19:02 37:38=ð0:0083145ðT þ 273:15ÞÞ
where T is the temperature (C). The value of 270 ppm [CO2]
approximates the preindustrial atmosphere, 350 ppm [CO2] reflects
the recent atmosphere and 700 ppm [CO2] is a possible future (and
distant-past) atmospheric value. The fraction of CO2 assimilated,
which is subsequently released as CO2 through photorespiration, is
0.5vO ⁄ vC, and so the ratio vO ⁄ vC = 1 corresponds to 50% loss of
assimilated CO2 to photorespiration. (b) Theoretical quantum
requirements for C3 leaf CO2 assimilation (i.e. net CO2 assimilation,
or photosynthesis minus photorespiration, in the absence of
respiration) as a function of temperature and ambient [CO2], as in
(a). The continuous lines correspond to photophosphorylative
H+ ⁄ ATP = 4 and the curved dashed line corresponds to
H+ ⁄ ATP = 14 ⁄ 3 (and [CO2] = 700 ppm). The lower horizontal
dashed line is the theoretical minimal C3 quantum requirement (i.e.
without photorespiration) of 8.17 photon ⁄ CO2 (with H+ ⁄ ATP = 4).
The upper horizontal dashed line (=13.02 photon ⁄ CO2) corresponds
to a C4 leaf with vO ⁄ vC = 0.03, CO2 overcycling = 0.10 and H+ ⁄ ATP =
4 (Table 3). All lines correspond to the production of sucrose.
crops: maize, sugarcane, sorghum and millet. This C4 cycle,
which is a preface to C3 photosynthesis in C4 leaves, requires
two ATP to assimilate a CO2 in the mesophyll, release it in
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Quantum requirements are for the photosynthesis of sucrose,
accounting for photorespiration. The C4 system corresponds to
NADP-malic enzyme-type C4 species (e.g. maize, sugarcane,
sorghum). vO ⁄ vC is the oxygenation ⁄ carboxylation ratio of ribulose
1,5-P2. C4 overcycling replaces CO2 delivered to bundle sheath cells
via the C4 cycle which subsequently leaks out of these cells. Entries
of zero for vO ⁄ vC or C4 overcycling are absolute minima that are not
expected in nature. Results are shown for photophosphorylative
H+ ⁄ ATP = 14 ⁄ 3 (in addition to H+ ⁄ ATP = 4) as a gauge of its
potential significance; this review tentatively rejects it as a likely
value in extant plants (see text).
the bundle sheath and regenerate the CO2 acceptor (Hatch,
1987; Kanai & Edwards, 1999; Table S5). Some CO2 leakage from bundle sheath cells is inevitable (Hatch et al.,
1995), so that the C4 cycle operates more rapidly (‘C4 overcycling’) than the C3 cycle in C4 plants. Apparently, there is
no theoretically determined minimal overcycling amount. A
minimal experimental value is c. 10% (von Caemmerer,
2000). With 10% overcycling, C4 photosynthesis would
require 2.2 ATP ⁄ CO2 more than C3 photosynthesis
(NADPH requirements are equal). This ‘extra’ ATP is
assumed to come from cyclic photophosphorylation in bundle sheath chloroplasts (Hatch, 1987; Laisk & Edwards,
2000). Thus, simultaneous operation of LET and CET
occurs for C4 photosynthesis, with LET confined mainly to
mesophyll cells and CET to bundle sheath cells (Hatch,
1987). In either C3 or C4 systems, CET activity requires
that PS I absorb more photons than PS II at the whole-leaf
scale, which is observed (Nelson & Yocum, 2006). In addition, the spatial organization of PS I and PS II within
thylakoids may be conducive to simultaneous LET and
CET inside a single chloroplast (Dekker & Boekema,
2005), but significant C3 leaf CET activity is controversial
(Joliot & Joliot, 2002; Munekage et al., 2004; Johnson, 2005).
By concentrating CO2 in the bundle sheath (where rubisco operates in C4 leaves), photorespiration is suppressed,
but not eliminated. The minimal (potential) rate is
unknown, but maize experiments indicate vO ⁄ vC of c. 0.03
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with normal CO2 supply (de Veau & Burris, 1989); this
value is used herein.
The C4 plant quantum requirement is calculated as above
for C3 plants with the ‘extra’ ATP requirement for the C4
cycle (with overcycling) added to QR,C. For vO ⁄ vC = 0.03
and C4 overcycling of 0.10, the C4 quantum requirement is
c. 13 photon ⁄ CO2 with H+ ⁄ ATP = 4, but c. 14.8 photon ⁄
CO2 with H+ ⁄ ATP = 14 ⁄ 3 (Table 3). In contrast with C3
plants, the C4 plant quantum requirement is largely insensitive to temperature and [CO2] because vO ⁄ vC is stable.
5. Uncertainty about H+ ⁄ ATP and its importance
An eight-photon requirement (per CO2) for NADPH
production appears to be fixed, but the photon ⁄ ATP stoichiometry is less clear. It depends on the number of protons
deposited in the lumen per absorbed photon (H+ ⁄ photon)
and H+ ⁄ ATP. Thirty years ago, it was widely accepted
(reviewed by Farquhar & von Caemmerer, 1982) that LET
accumulated one (rather than 1.5) proton in the lumen per
absorbed photon, H+ ⁄ ATP was three (rather than four or
14 ⁄ 3) and CET pumped one (rather than two) proton per
absorbed photon. With these assumptions, C3 sucrose photosynthesis would require 9.25 photon ⁄ CO2, which is more
than that observed in some apparently reliable quantum use
measurements (e.g. Walker & Osmond, 1986; Björkman &
Demmig, 1987; Evans, 1987) when modest allowance is
made for inactive absorption. The corresponding quantum
requirement for C4 photosynthesis (with only modest C4
overcycling and inactive absorption) would exceed some
measured quantum use values in C4 leaves (e.g. Ehleringer
& Pearcy, 1983).
Revisions (as above) to H+ ⁄ photon and H+ ⁄ ATP brought
theoretical calculations into line with the data, but the proposed 14 ⁄ 3 H+ ⁄ ATP stoichiometry re-raised the possibility
of a theoretical C3 quantum requirement exceeding nine
photon ⁄ CO2. Therefore, if it is accepted that H+ ⁄ photon is
1.5 for LET and two for CET, and that the ATP requirement for C3 photosynthesis is c. 3.1 ATP ⁄ CO2, the 14 ⁄ 3
H+ ⁄ ATP ratio is tentatively rejected for incompatibility with
seemingly reliable leaf-level quantum use measurements.
Further calculations herein are therefore confined to a
photophosphorylative H+ ⁄ ATP ratio of four.
6. C3 vs C4 photosynthesis
When vO ⁄ vC is small, C3 plants have a smaller quantum
requirement than C4 plants. Once C3 leaf vO ⁄ vC exceeds c.
0.32, however, the theoretical minimum C4 quantum
requirement becomes superior (Table 3). As presently calculated, this should occur at temperatures above c. 23C
with 350 ppm atmospheric [CO2] (Fig. 3), which is consistent with experimental estimates of quantum use in C3 and
C4 leaves (Ehleringer & Björkman, 1977; Ehleringer &
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Pearcy, 1983). As atmospheric [CO2] continues to increase,
the quantum requirement of C3 plants should decline, with
little effect on C4 plants. At 700 ppm CO2, the temperature
at which the quantum requirement for C4 photosynthesis
becomes superior (i.e. smaller than the C3 quantum
requirement) increases to nearly 37C with the biochemical
parameters underlying Fig. 3.
7. Theoretically maximal efficiency of photosynthesis
For daylight containing 4.57 mol photons MJ)1 PAR, a C3
leaf at 30C and 350 ppm atmospheric [CO2] (i.e. vO ⁄ vC 0.45) could photosynthesize c. 0.025 mol sucrose MJ)1
absorbed PAR (excluding inactive absorption). Sucrose contains 5.643 MJ mol)1 (Table S1), and so the efficiency of
photosynthesis (including photorespiration) could be as high
as 0.140 J J)1 absorbed PAR. For C3 photosynthesis of
starch (2.835 MJ mol)1 glucose residue), the potential efficiency is 0.139 J J)1. At 20C, the potential C3 efficiencies
increase to 0.179 J J)1 (sucrose) and 0.177 J J)1 (starch).
The potential efficiency of C4 photosynthesis (vO ⁄ vC =
0.03, C4 overcycling = 0.10) of sucrose is 0.165 J J)1
absorbed PAR. For starch, the potential efficiency is
0.163 J J)1. This indicates that as much as c. 16–18% of
the energy in clear-sky PAR absorbed by photosynthetic
pigments could be retained in C3 and C4 photosynthesis
(for the conditions specified).
In addition to CO2, both NO3 and SO4 can be photosynthetically assimilated (Beevers & Hageman, 1969; Pate
& Layzell, 1990; Hell, 1997; Noctor & Foyer, 1998). SO4
assimilation is a minor fraction of plant energetics and is
included in amino acid biosynthesis below. If NO3 photoassimilation occurs, it could increase apparent QR, but theoretically by < 5% (Table S47). Plants absorbing NH3 from
the soil – the most efficient case, and the case adopted
herein – need not expend energy for NO3 reduction, but
other considerations arise (see Raven, 1985).
V. Respiration
Analyses of potential solar-energy-use efficiency sometimes
treat respiration simply as a fraction (typically 30–40%) of
photosynthesis (e.g. Loomis & Williams, 1963; Long et al.,
2006; Zhu et al., 2008). (It may be of interest that Bonner’s
(1962) discussion of ‘the upper limit of yield by the world’s
crop plants’ did not once mention respiration). A
better approach is to quantify theoretical stoichiometries of
respiratory reactions ⁄ pathways and numerically relate them
to essential growth and maintenance processes. Although a
simple respiration : photosynthesis ratio may sometimes
adequately summarize experimental data (Gifford, 1995),
it need not provide insights into potential efficiency.
Moreover, as Beevers (1970) noted: ‘understanding...of respiration has progressed to the point where it is no longer
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Intermembrane
space
Inner
membrane
4 H+
Complex I
Mitochondrial
matrix
NADH
4 H+
NAD
NADH
NADH
DH
NAD
2e–
NADPH
NADPH
DH
NADP
UQ
Pool
2e–
2
H+
Complex III
NADH
NADH
DH
NAD
FADH 2
Complex
II
2 H+ +
0.5 O2
Alt.
oxidase
2
FAD
H2O
H+
cyt c 2e–
4 H+
ATP
ADP
Antiporter
H+
Pi
Symporter
x H+
F0
Pyruvate
H+
H+ + HCO3
0.5 O2 + 2 H+
4 H+
H2O
Complex IV
Symporter
ATP
ADP
H+
Pi
ATP
x H+
F1
Pyruvate
H+
CO2 + H2O
necessary or proper to regard this process simply as a black
box, a negative quantity in the equation for plant yield’.
Respiration [i.e. glycolysis, the oxidative pentose phosphate pathway (OPPP), TCA cycle, mitochondrial electron
transport chain (mETC) and oxidative phosphorylation]
produces ATP, NAD(P)H, CO2 and heat. It also supplies
carbon skeleton precursors of growth (Beevers, 1961), but
this function is explicitly dealt with below (Substrate
requirement for growth); the immediate issue is ATP and
NADPH provision.
1. ATP production from sucrose oxidation
Perhaps the most frequently mentioned metabolic stoichiometry in eukaryotic metabolism is the amount of ADP that
can be phosphorylated during the oxidation of respiratory
substrate, often glucose. Only since c. 1990 has it become
generally accepted (but not universally appreciated) that the
ratio of ATP formed per glucose oxidized is less than the ‘traditional’ c. 36 ATP ⁄ glucose (or equivalently c. 72 ATP ⁄
sucrose) (Hinkle et al., 1991). How much less is debated.
Starting with sucrose, glycolysis initiated by invertase can
produce (per sucrose): four pyruvate, four ATP and
four NADH (Table S6a). One additional ATP (per sucrose)
can be formed if sucrose synthase initiates glycolysis
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Fig. 4 Schematic diagram of the mitochondrial electron transport
chain (mETC), proton translocation across the inner mitochondrial
membrane and oxidative phosphorylation. The ‘UQ pool’ (within
the inner membrane) is composed of ubiquinone (UQ) and reduced
UQ (UQH2), which are electron acceptor and donor, respectively.
UQ can be reduced by five dehydrogenases (DHs). Complex I
oxidizes matrical NADH, reduces UQ and translocates four protons
across the inner membrane for each NADH oxidized, that is for each
electron pair (2e)) transported (Galkin et al., 2006). Matrical NADH
can also be oxidized by a second matrix-facing NADH DH, which
does not translocate protons (Douce & Neuburger, 1989). Complex
II, the only enzyme that is both part of the TCA cycle and mETC,
oxidizes succinate (forming fumarate) by reducing FAD to FADH2
(FAD is a Complex II component). Complex II does not translocate
protons. Cytosolic (intermembrane space) NADH and NADPH can
be oxidized by cytosol-facing NADH and NADPH DHs, reducing UQ
(Douce & Neuburger, 1989). UQH2 donates electrons to either
Complex III or alternative (Alt.) oxidase; the latter does not
translocate protons. In each case, one water molecule is formed
from free oxygen for every NADH, FADH2 or NADPH oxidized; this
is analogous, but opposite in ‘direction’, to photosynthetic water
splitting, in which two electrons are extracted from water,
producing free oxygen, to reduce one NADP molecule. Complex III
reduces cytochrome (cyt) c and Complex IV oxidizes cyt c.
Together, Complexes III and IV translocate six H+ ⁄ 2e) (a Q-cycle is
assumed), partitioned for convenience as two and four in the
schematic diagram (Trumpower, 1990; Wikström, 2000; Brand,
2005; Hinkle, 2005). ADP is phosphorylated by F1F0-ATP synthase,
which translocates x (i.e. H+ ⁄ ATP) protons into the mitochondrial
matrix per ADP phosphorylated. The value of x is debated, with
three and 10 ⁄ 3 (c. 3.33) currently cited (see text). ATP is exported
from the matrix in exchange (antiport) for ADP, and each ADP
entering the mitochondrial matrix is accompanied by a Pi
transported with a proton (symport). (This is an important difference
between chloroplasts and mitochondria: photophosphorylation
takes place within the chloroplast stroma, where most of the
resulting ATP is used, and oxidative phosphorylation occurs in the
mitochondrial matrix, but much of the resulting ATP is used
elsewhere.) Mitochondrial uptake of pyruvate (the main TCA cycle
substrate) is coupled to proton symport (Papa et al., 1971), but
LaNoue & Schoolwerth (1979) proposed that the proton influx is
balanced by the efflux of CO2 (the product of pyruvate oxidation)
and its conversion to carbonic acid (and proton generation) outside
the mitochondria. Leaks and slips (Brand, 2005), which reduce
efficiency, are ignored here. Much present knowledge of mETC is
from research with animals and microbes; it is implicit that the
mechanisms and stoichiometries are similar in plants.
(Table S6b). Using four pyruvates, the TCA cycle can produce four ATP in substrate-level phosphorylations, 16
NADH, four FADH2 and 12 CO2 (Table S7). NADH
(from glycolysis and the TCA cycle) and FADH2 can be
oxidized via mETC, resulting in translocation of up to 208
protons (per sucrose) out of the mitochondrial matrix
(Fig. 4). Four protons are used to import Pi (symport)
needed for the four substrate-level phosphorylations, but
the remaining 204 protons are available to drive oxidative
phosphorylation via their flux back into mitochondria
though F1F0-ATP synthases.
The H+ ⁄ ATP ratio of mitochondrial ATP synthases was
experimentally estimated to be c. two several decades ago
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and then revised to c. three (Ferguson & Sorgato, 1982;
Berry & Hinkle, 1983; Nicholls & Ferguson, 1992; Brand,
2005; Hinkle, 2005). The recent determination that F0
rings in yeast mitochondria have 10 c subunits (Stock et al.,
1999), compared with 14 in chloroplasts, indicates that,
mechanistically, H+ ⁄ ATP may be 10 ⁄ 3 (c. 3.33) for mitochondrial ATP synthases. In view of the tentative rejection
of the mechanistic 14 ⁄ 3 H+ ⁄ ATP value for photophosphorylation above, however, the experimental H+ ⁄ ATP of three
(rather than the mechanistic ratio 10 ⁄ 3) is adopted herein
for oxidative phosphorylation (but see Brand, 2005;
Hinkle, 2005). By including the proton imported into
mitochondria with each Pi (Fig. 4), the total proton
requirement per oxidative phosphorylation becomes 1 +
H+ ⁄ ATP, or about four. Thus, 51 ATP could be produced
by the 204 protons above through oxidative phosphorylation (c. 47 ATP if H+ ⁄ ATP is 10 ⁄ 3). The ratio of ATP
formed per sucrose oxidized (YATP,sucrose, ATP ⁄ sucrose) is
then 59 if glycolysis is initiated by invertase, and 60 for
sucrose synthase-initiated glycolysis. YATP,sucrose = 59.5 ATP ⁄
sucrose is used herein to represent efficient respiration (equivalent, for historical comparison, to 29.75 ATP ⁄ glucose).
Although the operational H+ ⁄ ATP ratios of photophosphorylation and oxidative phosphorylation are similar (or
identical) when accounting for the H+-Pi symport associated with oxidative phosphorylation, the H+ ⁄ ATP values of
the ATP synthases themselves differ. This may appear
strange. Even if the F0 c-subunit number, call it z, does not
define H+ ⁄ ATP in the exact ratio z ⁄ 3, the relative difference
in c-subunit number may be related to relative H+ ⁄ ATP.
But ‘why’ should H+ ⁄ ATP differ between chloroplasts and
mitochondria? The reader is directed to von Ballmoos et al.
(2009) for a brief speculation on this question.
ical closed cycle of OPPP (Beevers, 1961) oxidizing sucrose,
summarized by (Table S8a):
Sucrose þ 2 ATP þ 24 NADP
! 24 NADPH þ 2 ADP þ 2 Pi þ 12 CO2 :
Substituting 2 ⁄ YATP,sucrose for ‘2 ATP’ gives the
relationship for NADPH formed per sucrose
oxidized (YNADPH,sucrose, NADPH ⁄ sucrose) as 24 ⁄ (1 + 2 ⁄
YATP,sucrose), which is c. 23.2 NADPH ⁄ sucrose with
YATP,sucrose = 59.5. Although closed-cycle OPPP operation
may be atypical, this definition of YNADPH,sucrose is a useful
quantification of sucrose requirement for NADPH production (e.g. Williams et al., 1987).
4. Alternative oxidase
The mitochondrial alternative oxidase short circuits mETC,
reducing proton translocation out of the matrix (Fig. 4)
and, although it appears wasteful, it may provide benefit
(Vanlerberghe & McIntosh, 1997; Robson & Vanlerberghe,
2002). If it accounts for one-half of respiratory O2 uptake,
c. 30% of the potential for respiratory ATP production is
lost, but the measurement of alternative oxidase activity
is difficult (Day et al., 1996; Florez-Sarasa et al., 2007).
The key missing element is the quantification of its required
engagement.
My interpretation of the data in Millar et al. (1998) is
that rapidly growing cells can avoid alternative oxidase
engagement. Growth calculations herein therefore ignore it
(i.e. YATP,sucrose = 59.5 for potential growth processes).
Significant engagement (25–50% of O2 uptake) may be
associated with maintenance, however (Millar et al., 1998;
Florez-Sarasa et al., 2007).
2. ATP production from ‘excess’ NADH
Many biosynthetic pathways generate net NADH (e.g.
Tables S12–S14, S23, S24, etc.). These pathways require
NAD regeneration for continued operation. The coupling
of the oxidation of ‘excess’ NADH to ADP phosphorylation
can be expedient.
Excess NADH is formed mainly in the cytosol and plastids, and presumably has access to the cytosol-facing NADH
dehydrogenase on the inner mitochondrial membrane
(Fig. 4), perhaps via NAD ⁄ NADH shuttles for plastidic
NADH. The maximal ratio of ATP formed per cytosolic
NADH oxidized by mitochondria (YATP,NADH-C, ATP ⁄
NADH) is 6 ⁄ (1 + H+ ⁄ ATP), which is 1.5 ATP ⁄ NADH
(with H+ ⁄ ATP = 3).
3. NADPH production from sucrose oxidation
The main biosynthetic electron donor is NADPH. Its
source (outside of photosynthesis) is taken to be a hypothet-
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VI. Photosynthate mobilization and
translocation
The mobilization of chloroplastic starch and the translocation of sucrose via the phloem require ATP, which, in this
analysis, comes from respiration. This respiration is quantitatively important to night-time source leaf metabolism
(Bouma et al., 1995; Noguchi et al., 2001).
The cost of starch mobilization depends on the reactions
involved (Noguchi et al., 2001); herein, chloroplastic starch
is converted to sucrose via maltose (Chia et al., 2004; Weise
et al., 2004; Smith et al., 2005), summarized by (Table S9):
ðstarchÞn þ 2 ATP ! sucrose þ ðstarchÞn2 þ 2 ADP þ 2 Pi
where (starch)n indicates a starch polymer of n glucose residues. Thus, 2 ⁄ YATP,sucrose sucrose are respired to mobilize
each sucrose unit (starch fi sucrose), giving a potential
YE of c. 0.963 for mobilization as follows: product is one
sucrose (5.6434 MJ mol)1), substrate is two starch units
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(5.6698 MJ in 2 mol units) plus 2 ⁄ YATP,sucrose mol sucrose
for respiration to supply ATP (0.1897 MJ in 2 ⁄ YATP,sucrose
mol sucrose), giving 5.6434 ⁄ (5.6698 + 0.1897) 0.963
(see Table S1 for heats of combustion).
The ATP required for phloem translocation depends on
the number of active membrane crossings and the cost of
each crossing (Amthor, 1994; Patrick, 1997; van Bel,
2003). Minimal values may be one active crossing and one
ATP per crossing, giving a potential YE of c. 0.983 for the
process. For plants that require temporary storage between
sources and (future) sinks (e.g. starch and protein stored in
stems and later mobilized for seed growth), additional
mobilization and translocation costs are needed (Penning
de Vries et al., 1983).
For photosynthesis producing 30% starch and 70%
sucrose, the overall potential (maximal) efficiency of mobilization plus translocation to sinks may be YE 0.973.
moderate temperature, is set to 15% of photosynthate
remaining after mobilization and translocation (see Loomis
& Amthor, 1999). To account for lower C4 plant protein
concentration, and presuming a relationship between protein concentration and maintenance needs (Amthor, 1994),
the speculative C4 plant minimum is set to 12% of photosynthesis. These values are meant to reflect maintenance
requirements of healthy, rapidly growing plants and to
include both ‘structure maintenance’ and ‘tool maintenance’ (Penning de Vries et al., 1974), and assume that
maintenance metabolism acclimates effectively to temperature fluctuations (Gifford, 1995). Any required alternative
oxidase activity, which appears to be important to actual
maintenance respiration (Florez-Sarasa et al., 2007), is
implicit in these values.
VII. Maintenance
Substrate requirement for growth is the amount of sucrose
needed to provide carbon skeletons, ATP and NADPH for
synthesis of a compound, or whole plant, including polymerization reactions. Theoretically minimal substrate
requirements are calculated by tracing the most efficient biochemical pathways from sucrose (or, historically, glucose) to
specific products (e.g. cellulose or proteins), accounting for
any net ATP and ⁄ or NAD(P)H needed (e.g. Penning de
Vries et al., 1974, 1983; Thornley & Johnson, 1990;
Amthor, 2003). For whole tissues ⁄ plants, substrate requirements for individual (classes of) compounds are summed in
proportion to phytomass composition (Thornley & France,
2007). To derive the approximate whole-plant substrate
requirement, therefore, representative values are needed for
cellulose, hemicelluloses, lignins, proteins, lipids, organic
acids and, in some plants, pectins and ⁄ or storage carbohydrates (Penning de Vries et al., 1974, 1983). The cost of
mineral uptake is also needed. All of these classes of compound are considered briefly below; more detail will sometimes be needed (e.g. if significant amounts of storage lipids
or secondary compounds are synthesized).
The amount of substrate produced by photosynthesis
(minus photorespiration, respiration supporting translocation and maintenance respiration) divided by the substrate requirement for growth dictates potential growth.
Phytomass composition dictates DHC and, with substrate
requirement, determines potential YE of growth. Because
most carbon and energy in biosynthetic substrates are
retained in end products during growth, substrate requirements are not proportional to YATP,sucrose (Penning de Vries
et al., 1983).
Life requires maintenance to counteract local entropy and
to acclimate to environmental fluctuations. This includes
the regular replacement of enzyme and lipid populations
with different populations better suited to new conditions
and developmental states, active transport to counteract
leaks, repair of damage from, for example, endogenous and
exogenous oxidants, and repair ⁄ replacement of compounds
subject to spontaneous breakdown. ‘Maintenance respiration’ is the CO2 and energy release associated with maintenance processes (Penning de Vries, 1975). An efficient
plant would circumvent unnecessary molecular turnover
and leaks, and would carry out maintenance with maximal
YATP,sucrose.
In principle, the calculation of energy use (photosynthate
consumption) for maintenance is straightforward. For example, if one ATP is expended to pump one ion across a membrane, a leak of x ions will require x ATP (or x ⁄ YATP,sucrose
sucrose) for ion gradient maintenance. In practice the task is
difficult. Although a bold theoretical assessment of actual
maintenance respiration was made decades ago (Penning de
Vries, 1975; Penning de Vries et al., 1983), a lack of data on
essential (minimal) turnover and transport processes still precludes the quantification of minimal maintenance needs
(Nelson, 1994). As more quantitative data become available
for underlying maintenance processes, such as protein
turnover (Piques et al., 2009), theoretical re-evaluations of
maintenance requirements can be conducted.
In spite of criticizing above the use of simple respiration : photosynthesis ratios, the quantification of minimally
required maintenance respiration is now hedged because a
maintenance requirement must be specified for the present
analysis. From a personal perspective on data and theory
(Amthor, 2000), a daily sucrose requirement for essential
maintenance metabolism of nonwoody C3 plants, at
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VIII. Substrate requirement for growth
1. Cellulose
Cellulose consists of long chains of b(1fi 4)-linked glucose
residues and may be nature’s most abundant polymer.
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Although questions about cellulose biosynthesis remain
(Somerville, 2006), the calculation of its substrate requirement is now simple. It is synthesized at the plasmalemma
from cytosolic sucrose by the coordinated action of just two
enzymes: sucrose synthase and cellulose synthase. The net
transformation is:
ðcelluloseÞn þ sucrose ! ðcelluloseÞnþ1 þ fructose
where (cellulose)n indicates a cellulose polymer composed
of n glucose residues. Apart from the maintenance of associated enzymes and sucrose delivery, cellulose synthesis
involves no ATP or reductant. Assuming that the fructose
formed (released into the cytosol) is available as substrate
elsewhere, potential YE is c. 0.993 (Table 4).
Traditional substrate requirement calculations (e.g.
Penning de Vries et al., 1974; Williams et al., 1987) were
summarized as:
ðcelluloseÞn þ glucose þ 2 ATP ! ðcelluloseÞnþ1
Together with the traditional estimate of 36 ATP ⁄
glucose resulting from respiration, YE would then be 0.95
Table 4 Calculated potential efficiencies of energy use (YE) during
the biosynthesis of polysaccharides and lignins from sucrose
Polymer or monomer residue
YE (J J)1)
Cellulose
Starch (storage organ)
Hemicelluloses (residues)
Arabinose
Xylose
Fucose
Galactose
D-Glucose
Glucuronate
Glucuronate (methylated)
Mannose
Rhamnose
Lignins (residues)
p-Coumaryl alcohol
Coniferyl alcohol
Sinapyl alcohol
0.993
0.972
0.865
0.867
0.865
0.938
0.938
0.865
0.802
0.940
0.865
2. Hemicelluloses and pectins
Hemicelluloses are semi-random polysaccharide heteropolymers (except glucans, which are composed entirely of glucose residues) that vary among species, tissues, and primary
and secondary cell walls (Scheller & Ulvskov, 2010). They
may, as a group, be as abundant as cellulose.
Hemicelluloses are synthesized from NDP-hexoses and
UDP-pentoses. Monomer synthesis (Tables S11–S18) is
mainly cytosolic. For polymerization (Table S19), NDPsugars are imported into Golgi bodies in antiport with corresponding NMPs; NDPs are cleaved from the imported
sugars and hydrolyzed to NMP and Pi, providing energy for
the polymerization of the sugars (Orellana et al., 1997;
Wulff et al., 2000); and the cytosolic NMP is converted to
NDP using ATP. An expensive methylation of some glucuronate residues occurs (Table S20).
Potential YE values for individual sugar residues within
hemicelluloses cover the range 0.80–0.94 (Table 4). The
most efficiently produced hemicelluloses should be glucans,
galactomannans and galactoglucomannans, but many hemicelluloses are based on the less efficiently produced xylose
residue, which presumably confers some advantage(s).
Pectins are polysaccharides that cement other cell wall constituents. They are relatively important in dicots, but only a
minor component of grass cell walls. Homogalacturonan
(with some of its carboxyl groups methylated) is a major pectin type (Ridley et al., 2001; Wolf et al., 2009). Its theoretical
substrate requirement is the same as that of glucuronate (and
its methylated form) in hemicelluloses.
3. Lignins
0.831
0.737
0.674
Calculations based on YATP,sucrose = 59.5 ATP ⁄ sucrose, YATP,NADH-C =
1.5 ATP ⁄ NADH and YNADPH,sucrose 23.2 NADPH ⁄ sucrose. For
cellulose, YE is given by (DHC cellulose) ⁄ (DHC sucrose – DHC fructose). For all others, YE is given by (DHC residue in polymer) ⁄ (DHC in
sucrose requirement); see Supporting Information Table S1 for DHC
values used. Starch results are derived from Table S10. Values for
residues are after polymerization and include (estimated) residue–
residue bond energies. For hemicelluloses, this residue–residue bond
energy was 0.019 MJ mol)1, which was based on a comparison of
DHC values of cellulose and starch with the values for free glucose.
For lignins, the residue–residue bond energy was assumed to be
0.015 MJ mol)1. Results for hemicellulose residues are based on
Tables S11–S20. Results for lignin residues are from equations S.2,
S.5, S.7, S.9, S.27, and the average of equations S.11–S.16 in
Amthor (2003) evaluated with the respiratory stoichiometries given
above.
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rather than 0.99; with an up-to-date 29.75 ATP ⁄ glucose
value (from above), it would further decline to 0.94. It is
therefore quantitatively important to designate sucrose as
the biosynthetic substrate (Thornley & France, 2007).
Lignins are formed mainly from three cinnamyl alcohols.
They are especially important in wood. If the most recent
theoretical analysis of lignin biosynthetic efficiency
(Amthor, 2003) is updated with respiratory stoichiometries and DHC values from above, potential YE values of
the polymerized monomers cover the range 0.67–0.83
(Table 4).
4. Starch (long-term storage)
More than one-half of seed and tuber mass can be starch,
which is synthesized from ADP-glucose, requiring one ATP
per glucose residue polymerized (Smith et al., 1997;
Table S10). Potential YE is 0.97 (Table 4). Traditional calculations (e.g. Thornley & Johnson, 1990) involved twice
the ATP, resulting in smaller YE.
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5. Proteins
Sucrose and NH3 are the designated substrates for amino
acid synthesis. Herein, invertase cleaves sucrose to initiate
the process (Tables S21–S42). Cysteine synthesis also
requires sulfur; SO4 uptake and reduction costs are included
in cysteine synthesis calculations (Table S30). Methionine,
the other sulfur-containing amino acid, is made from
cysteine (Table S41).
Polymerization probably requires at least 4.5 ATP ⁄
amino acid (Zerihun et al., 1998; Amthor, 2000). With
YATP,sucrose = 59.5, at least 0.42 MJ are needed per mole
of peptide bond formed. If peptide bonds contain
c. 0.0075 MJ mol)1 (Rawitscher et al., 1961), < 2% of the
energy used for polymerization is retained in the polymer.
For amino acid residues within proteins, potential YE
covers the range 0.55–0.81 (Table 5). Variation in amino
acid composition of the myriad plant proteins causes variation
in whole-protein YE. For nine important plant enzymes (as
examples), potential YE values varied over the modest range
0.726–0.737 (Table 6), but, for storage proteins (which can
have unique compositions; Shewry et al., 1995), variation in
YE is larger (not shown). DHC also varies among proteins.
The measured DHC values of 19 storage proteins covered the
range 22.4–24.8 MJ kg)1 (Benedict & Osborne, 1907),
whereas the calculated values for nine enzymes were in the
range 24.2–25.3 MJ kg)1 (Table 6). For present purposes,
protein in grasses is assigned YE = 0.73 and DHC =
24.5 MJ kg)1.
6. Lipids
Only a small fraction of most vegetative cells is lipid, but
the lipid concentration of some fruits and seeds is high
(Pritchard & Amthor, 2005). For 11 plant lipids, YE
covered the range 0.79–0.89 (derived from Williams et al.,
1987; Thornley & Johnson, 1990). A YE value of 0.87
(central tendency) is adopted as representative of lipids in
vegetative tissues and low-lipid seeds.
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Table 5 Calculated potential efficiencies of energy use (YE) during
amino acid synthesis from sucrose, NH3 and SO4, and polymerization
into protein
YE (J J)1)
Amino acid
Amino acid1
Polymerized
residue1
Alanine
Arginine
Asparagine
Aspartic acid
Cysteine
Glutamate
Glutamine
Glycine
Histidine
Isoleucine
Leucine
Lysine
Methionine
Phenylalanine
Proline
Serine
Threonine
Tryptophan
Tyrosine
Valine
0.904
0.737
0.755
0.848
0.684
0.810
0.790
0.716
0.718
0.848
0.893
0.864
0.662
0.854
0.815
0.829
0.813
0.806
0.852
0.910
0.733
0.681
0.649
0.695
0.607
0.705
0.700
0.550
0.656
0.772
0.809
0.787
0.614
0.793
0.725
0.670
0.699
0.760
0.789
0.805
Calculations based on YATP,sucrose = 59.5 ATP ⁄ sucrose, YATP,NADH-C =
1.5 ATP ⁄ NADH and YNADPH,sucrose 23.2 NADPH ⁄ sucrose.
Polymerization cost was set to 4.5 ATP ⁄ amino acid and the peptide
bond energy content was set to 0.0075 MJ mol)1 (see text). YE is
the energy in free amino acid or amino acid residue (including
peptide bond energy) divided by the sum of energies in the sucrose
and NH3 required for their synthesis (and polymerization for residues). Substrate, amino acid and amino acid residue DHC values
were from Supporting Information Table S1 (amino acid and amino
acid residue DHC values are the same per mole and per mole carbon;
they differ per kilogram only to the extent that free amino acids
contain 0.018015 kg mol)1 (i.e. 1 mol H2O) more than the
corresponding residue).
1
, ‘Amino acid’ indicates the free monomer; ‘polymerized residue’
indicates the residue within a protein, including the ATP required for
polymerization and the estimated peptide bond energy.
The free energy per carbon atom in organic acids is relatively small (Table 2). The calculated YE values of the four
main organic acids in plants span the range 0.86–0.96
(derived from Tables S1 and S43–S46).
mass of minerals (related to ash remaining after combustion)
is herein assumed to be 25 g mol)1 and the minimal net
uptake cost is set to 0.75 mol ATP mol)1; this entails passive uptake of some species (modified after Thornley &
France, 2007). For NO3 uptake, two ATP ⁄ NO3 might be
required (Clarkson, 1985), but maximal solar-energy-use
efficiency may occur when NH3 is the nitrogen source.
8. Minerals
9. Whole plants
Minerals make up the final ‘major’ fraction of phytomass.
Their uptake from the soil solution is energetically important (Clarkson, 1985), but estimates of minimal energetic
requirements are rare. Variation in plant mineral content
(Epstein, 1994) is a complication. The mean molecular
Phytomass composition differs among species and environments, causing a range of theoretical substrate requirements
(e.g. Penning de Vries et al., 1983; Poorter et al., 1997); no
single value is appropriate for plants in general. To carry out
the present analysis, generic compositions of C3 and C4
7. Organic acids
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Table 6 Calculated potential efficiencies of energy use (YE) during the synthesis of specific enzymes (from sucrose, NH3 and SO4) and their
heats of combustion (DHC)
Protein
Calculated result
)1
YE (J J )
DHC (MJ kg)1)
A
B
C
D
E
F
G
H
I
0.737
25.30
0.726
24.45
0.730
24.51
0.729
24.58
0.731
24.42
0.731
24.75
0.729
24.18
0.735
24.18
0.733
24.60
Whole-protein YE and DHC values were calculated by summing the amino acid residue YE values from Table 5 and the DHC values from
Supporting Information Table S1 in proportion to the amino acid composition of each protein. The protein composition was derived from the
amino acid sequences available in UniProt Consortium (2009).
Proteins: A, cytochrome c oxidase subunit 2 from maize (UniProt accession P00412); B, rubisco large subunit plus rubisco small subunit PW9
from wheat (P11383 plus P26667); C, sucrose synthase from rice (P31924); D, nitrate reductase from Petunia hybrida (Q43042); E, PEP
carboxylase 1 from maize (P04711); F, cellulose synthase A catalytic subunit 6 [UDP-forming] from Arabidopsis thaliana (Q94JQ6); G, transketolase from potato chloroplast (Q43848); H, fructose-bisphosphate aldolase from Cicer arietinum cytosol (O65735); I, chloroplastic ATP
synthase from maize with F1 subunits in the ratio a3b3cde (with d chain from Sorghum vulgare) and F0 subunits in the ratio ab2c14 (P05022,
P00827, P0C1M0, Q07300, P00835, P17344, P48186, P69449).
grain crops were formulated, resulting in potential (maximal) whole-plant YE values of 0.869 and 0.879, respectively
(Table 7). The C3 system’s greater protein concentration
contributed to the C3–C4 difference.
It is notable that uncertainty about phytomass composition exists (in part) because measurement-based analyses of
plant make-up are typically unable to account for total mass
(e.g. Williams et al., 1987; Loomis & Connor, 1992; Poorter
et al., 1997). Another consideration is that older-organ
DHC is often less than that of younger organs (e.g. Williams
et al., 1987), and the biochemical composition also changes
(Thornley & Johnson, 1990). This may be related to secondary cell wall growth and ‘reorganization’ of structural
matter during development, with significant breakdown
and translocation (export) of structural constituents during
the final stage of development: senescence (Hopkins et al.,
2007). The effect of age on composition has implications
for the definition of substrate requirement; it should be
based on the composition of growing cells (see Thornley &
Johnson, 1990, p. 350–353).
Table 7 Calculated potential whole-plant YE and DHC of generic C3 and C4 grain crops
Plant constituent
or whole plant
Cellulose
Hemicelluloses
Lignins
Proteins
Lipids
Organic acids
Starch
Sucrose
Hexoses
Minerals
Whole plant
C3
C4
Fraction (kg kg)1)
YE (J J)1)
DHC (MJ kg)1)
Fraction (kg kg)1)
YE (J J)1)
DHC (MJ kg)1)
0.250
0.240
0.035
0.133
0.020
0.060
0.160
0.022
0.020
0.060
1.000
0.993
0.870
0.731
0.73
0.87
0.902
0.972
1.0
0.995
–
0.869
17.345
17.403
27.88
24.5
39.3
10.32
17.484
16.487
15.585
–
17.64
0.260
0.250
0.035
0.104
0.020
0.055
0.175
0.023
0.023
0.055
1.000
0.993
0.870
0.731
0.73
0.87
0.902
0.972
1.0
0.995
–
0.879
17.345
17.403
27.88
24.5
39.3
10.32
17.484
16.487
15.585
–
17.55
Columns labeled ‘fraction’ specify the contributions of individual constituents (i.e. compounds, classes of compound or minerals) to wholeplant dry mass. Values for whole-plant YE are whole-plant DHC divided by DHC of the weighted sum of sucrose (and NH3) requirements for
each component. The composition was formulated based on Penning de Vries et al. (1983), Lafitte & Loomis (1988) and Loomis & Connor
(1992) for a mixture of vegetative and reproductive phytomass; that is the composition is integrated over vegetative and reproductive growth
periods with significant production of starch in seeds. The biosynthetic substrates were sucrose, NH3 and SO4; YATP,sucrose was 59.5
ATP ⁄ sucrose, YATP,NADH-C was 1.5 ATP ⁄ NADH and YNADPH,sucrose was c. 23.2 NADPH ⁄ sucrose. Hemicellulose was taken to be 30% arabinose, 45% xylose, 10% glucose, 7% glucuronate, 6% methylated glucuronate and 2% mannose residues (based on data summarized in
Scheller & Ulvskov, 2010). Lignin was taken to be 20% p-coumaryl alcohol, 40% coniferyl alcohol and 40% sinapyl alcohol residues. The
organic acid fraction was taken to be 30% aconitic acid, 30% citric acid, 20% malic acid and 20% oxaloacetic acid. Hexoses were a 1 : 1 mix
of glucose and fructose. Minerals were assumed to have a mean molecular mass of 0.025 kg mol)1 and an uptake cost of
0.75 mol ATP mol)1 (see text), and so 0.504 mol sucrose was oxidized per kilogram of mineral taken up.
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IX. From sunlight to phyto-energy: potential
overall efficiency
1. Theoretical efficiency
The multiplication of component efficiencies gives wholeplant potential solar-energy-use efficiencies (Table 8) –
updates of Fig. 1(a). With respect to incident total solar
radiation and 350 ppm atmospheric [CO2], the calculated
potential solar-energy-use efficiency of the generic C3 grain
crop was 0.041 J J)1 at 30C and 0.053 J J)1 at 20C
(Table 8). The potential efficiency was 0.051 J J)1 for the
C4 grain crop (Table 8), which was assumed to be independent of temperature. If PAR is 48% of total solar radiation
and 93% of incident PAR is absorbed by a canopy, the
potential solar-energy-use efficiency is 2.24 times greater on
an absorbed PAR basis relative to incident total solar radiation. This applies to both C3 and C4 systems if both systems
absorb equal fractions of PAR. Relative to absorbed PAR,
therefore, potential efficiencies of the hypothetical C3 system were 0.092 J J)1 (at 30C) and 0.118 J J)1 (at 20C),
and that of the C4 system was 0.114 J J)1. The hypothetical
C4 system was potentially 23% more efficient than the C3
system at 30C, but, at 20C, the C3 system could be marginally more efficient. At greater [CO2], the efficiency of
the C3 (but not C4) system increases.
At 30C, the C3 plant efficiency based on absorbed PAR
was 12% smaller than the estimate in Zhu et al. (2008)
(Table 9). Much of this difference was a result of inactive
absorption of PAR in the present analysis; Zhu et al. (2008)
used 90% PAR absorption (rather than 93% in the present
analysis), but ignored inactive absorption. A small contribution to the difference arose from the 380 (rather than 350)
ppm [CO2] used by Zhu et al. (2008). The present absorbed
PAR-based C4 plant potential efficiency was 17% smaller
than in Zhu et al. (2008), which was a result of inclusion of
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inactive absorption, C4 overcycling and photorespiration in
the present analysis. All these processes occur in extant
plants (a criterion for this review), whereas Zhu et al.
(2008) targeted the maximum conceivable efficiency for C4
systems.
2. Measured efficiency
Analyses by Loomis & Gerakis (1975) and Monteith
(1978) among others showed that the maximal growth rates
of actual C4 systems are c. 40% faster than those of actual
C3 systems. Can this be reconciled with the present calculations of minimal C3 and C4 quantum requirements? Only
for photosynthesis at a temperature above 30C (with
atmospheric [CO2] of c. 350 ppm), because only then is the
minimal C4 quantum requirement far superior to (less
than) that of C3 systems (Fig. 3). This view is consistent
with the measured low-light quantum use in a range of C3
and C4 species, albeit with variation in the ‘crossover
temperature’ (e.g. Ehleringer & Björkman, 1977; Ehleringer
& Pearcy, 1983). It indicates that factors other than (in
addition to) quantum requirement are responsible for C3–
C4 growth rate differences, probably including faster lightsaturated C4 photosynthesis.
How do theoretical estimates of potential solar-energyuse efficiency derived here (Table 8) compare with field
measurements of, in particular, productive plant communities? For C3 systems in the field, efficiencies relative to incident total solar radiation of 0.032 J J)1 (rice), 0.044 J J)1
(soybean) and 0.045 J J)1 (sugarbeet [Beta vulgaris]) were
reported (Loomis & Gerakis, 1975). The rice value is c.
78% of the calculated potential C3 grain crop value at
30C, whereas the last two values exceed the potential calculated for 30C, but are c. 85% of the theoretical potential at
20C. These actual C3 crops were grown in atmospheres
with slightly lower [CO2] values, and therefore modestly
Table 8 Potential solar-energy-use efficiency of generic C3 and C4 grain crops
‘Process’ YE (J J)1)
C3
C4
‘Process’ linking incident total solar irradiance to production of new phyto-energy
20C
30C
Photosynthetically active radiation (PAR) fraction of incident total solar radiation
Canopy absorption of PAR
Fraction of PAR absorption by photosynthetic pigments
Photosynthesis (with photorespiration)
Photosynthate mobilization ⁄ translocation
Maintenance respiration
Efficiency of growth
Total (per unit incident total solar radiation)
Total (per unit absorbed PAR)
0.48
0.93
0.92
0.178
0.973
0.85
0.869
0.0525
0.1177
0.48
0.93
0.92
0.140
0.973
0.85
0.869
0.0412
0.0924
0.48
0.93
0.92
0.165
0.973
0.88
0.879
0.0509
0.1140
All incident solar radiation was assumed to be intercepted and photosynthesis (minus photorespiration) produced 30% starch and 70%
sucrose. Atmospheric [CO2] was 350 ppm.
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Table 9 Theoretical (quantum-based) estimates of potential solar-energy-use efficiency
Potential efficiency (J J)1)
Incident total solar radiation basis
Absorbed PAR basis
C3 system
C3 system
0.053
0.059
0.037–0.044
0.032
0.051
0.046
0.053
0.041
C4 system
0.050–0.058
0.043
0.060
0.060
0.051
0.12
0.14
0.093–0.098
0.068
0.118
0.105
0.118
0.092
C4 system
0.125–0.129
0.091
0.139
0.137
0.114
Notes
Source
(1)
(2)
(3)
(4)
(5)
(6)
(7)
20C
30C
A
A
B
C
D
E
F
This review
This review
Complete interception of incident solar radiation was assumed in all cases, but a range of assumptions were made about the fraction of photosynthetically active radiation (PAR) in solar radiation, absorption (and inactive absorption) of PAR, and respiration : photosynthesis ratio or
growth and maintenance requirements.
Notes: (1), Analysis conducted before adequate understanding of photorespiration and the metabolic differences between C3 and C4 plants. A
10-photon ⁄ CO2 quantum requirement was used. (2), Modified herein to account for differences in DHC of photosynthate and ash-free phytomass (see Fig. 1 and discussion in Loomis & Williams, 1963). (3), Based on quantum requirement of eight photon ⁄ CO2 for both C3 and C4
photosyntheses, vO ⁄ vC = 0.5 in C3 plants (0 in C4 plants), 25% loss of photosynthate (photosynthesis less photorespiration) to growth respiration and 25% loss of photosynthate to maintenance respiration. (4), A ‘practical estimate of maximum’ solar-energy-use efficiency accounting
for photorespiration, unavoidable light saturation of photosynthesis at 350 ppm atmospheric [CO2] (quantum requirement of 20
photon ⁄ CO2) and DHC of 17 MJ kg)1. (5), For a quantum requirement of 15.4 photon ⁄ CO2 (an empirical ratio including inactive absorption,
photorespiration and C4 overcycling), yield of the growth processes of 0.74 and DHC of 17.6 MJ kg)1. (6), At 25C. The C4 estimate is for
vO ⁄ vC = 0 and without C4 overcycling. (7), At 30C. The C4 estimate is for vO ⁄ vC = 0 and without C4 overcycling.
Sources: A, Loomis & Williams (1963); B, Beadle & Long (1985); C, Loomis & Amthor (1996); D, Loomis & Amthor (1999); E, Long et al.
(2006); F, Zhu et al. (2008).
larger quantum requirements, than used in the potential
efficiency calculations.
Efficiencies of actual C4 systems, again relative to incident total solar radiation, of 0.042 J J)1 (Pennisetum
typhoides) and 0.046 J J)1 (maize) were reported (Loomis
& Gerakis, 1975). The efficiency of 0.046 J J)1 is 90% of
the presently derived theoretical maximal value (see
Table 8) and 77% of the maximum potential efficiency
given by Zhu et al. (2008).
It is noteworthy that the maximum growth rate of the
maize crop mentioned by Loomis & Gerakis (1975) was
68% faster than the sugarbeet growth rate, but the solarenergy-use efficiencies were the same. Decoupling between
solar-energy-use efficiency and growth rate is related, at least
partially, to different amounts of incident solar radiation.
More recently, the measured efficiency of Miscanthus ·
giganteus (C4), with a whole-plant DHC of c. 18 MJ kg)1,
was c. 0.78 J J)1 intercepted PAR (Beale & Long, 1995).
That is c. 68% of the presently estimated theoretical potential on an absorbed PAR basis (Table 8), and c. 57% of the
potential estimated by Zhu et al. (2008). In intensively
managed maize, c. 3.8 g of above-ground phytomass accumulated per MJ absorbed PAR (Lindquist et al., 2005). If
allowance is made for 15% root mass (Anderson, 1988) and
whole-plant DHC of 17.5 MJ kg)1 (Lieth, 1968), the efficiency was c. 0.078 J J)1 relative to absorbed PAR (again c.
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68% of the presently calculated potential). Based on these
cursory comparisons, exceptional C3 and C4 plant communities may achieve a significant fraction of their potential
solar-energy-use efficiencies.
3. Respiration : photosynthesis ratio
Respiration : photosynthesis ratios of 0.30 (Zhu et al.,
2008), 0.33 (Loomis & Williams, 1963) and 0.40
(Monteith, 1977; Long et al., 2006) have been used to estimate potential efficiency. Finer distinctions recognizing
maintenance and growth respiratory components, with the
growth component on mechanistic grounds, were also used,
with resulting respiration : photosynthesis ratios of 0.30
(Loomis & Amthor, 1996; at a C3 quantum requirement of
15 photon ⁄ CO2), 0.36 (Loomis & Amthor, 1999; at a C4
quantum requirement of 16 photon ⁄ CO2) and 0.50
(Beadle & Long, 1985). Ratios derived from the present
analysis (Table 8) were 0.28 (C3 system) and 0.25 (C4 system), but these were free energy loss fractions of photosynthate, not CO2 losses. The carbon loss fractions were larger
because phytomass is more reduced than photosynthate. All
of these previous and present values were based on CO2
exchange measurements of crops, or were calculations based
on crop-plant composition. Different values may occur for
other plants, such as woody perennials.
The Author (2010)
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Phytologist
X. Assessment
Analyses of potential solar-energy-use efficiency based on
theoretically minimal quantum requirements – this review’s
subject – make no allowance for light saturation of photosynthesis, although it is expected in nature (Monteith,
1977). Moreover, assessments of upper limits on solarenergy-use efficiency involve quantitative uncertainties
about the potential efficiencies of processes underlying the
transduction of solar radiation into phyto-energy. Indeed,
as more processes are considered, and in more detail, overall
uncertainty can increase, which is a trait of research in
complex systems. In this light, the following points are suggested as key uncertainties and research needs:
• The fraction of PAR in solar radiation is place and time
specific.
• The amount of inactive PAR absorption is unclear, particularly at the canopy scale (senescing and dead leaves,
stems, and reproductive tissue, when present, probably
always contribute to whole-plant inactive absorption).
• Although a photophosphorylative H+ ⁄ ATP ratio of
14 ⁄ 3 may have a ‘mechanistic’ basis, it gives rise to apparently unrealistic quantum requirements when coupled with
the presently assumed stoichiometry between photon
absorption and proton deposition in the thylakoid lumen.
Resolving this issue may be important.
• If the mechanistic 14 ⁄ 3 photophosphorylative H+ ⁄ ATP
stoichiometry is incorrect, so too might be the 10 ⁄ 3 mechanistic H+ ⁄ ATP ratio for oxidative phosphorylation.
• Photorespiration and mitochondrial alternative oxidase
remain enigmas. They divert energy away from useful reactions, but may benefit plants. How much benefit is an
unanswered question.
• The theoretically minimal degree of C4 overcycling
remains unclear.
• The quantification of a theoretically minimal maintenance requirement is problematic and is a key contributor
to uncertainty about potential solar-energy-use efficiency.
• Exceptional plant communities may achieve a significant portion of their potential solar-energy-use efficiency,
but additional field-based measurements of incident (and
absorbed) solar radiation and resulting phyto-energy accumulation are needed to better understand differences
between potential and actual solar-energy-use efficiencies.
Acknowledgements
Thanks to Don Ort for helpful dialog, Bob Loomis for decades of encouragement, and two anonymous referees for
important suggestions.
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Supporting Information
Additional supporting information may be found in the
online version of this article.
Table S1 Heats of combustion of substrates and products,
including monomer residues within polymers
Table S2 (a) Reaction set for C3 photosynthesis of fructose
6-P; (b) reaction set for C3 photosynthesis of sucrose; (c)
reaction set for C3 photosynthesis of starch
Table S3 (a) Reaction set for photorespiration; (b) reaction
set for photorespiration modified to conserve energy
Table S4 Relating quantum requirement to the balance of
photosynthesis and photorespiration
Table S5 Reaction set for the C4 cycle in NADP-malic
enzyme-type C4 species
Table S6 (a) Reaction set for glycolysis initiated by invertase; (b) reaction set for glycolysis initiated by sucrose
synthase
Table S7 Reaction set for the TCA cycle within the mitochondrial matrix
Table S8 (a) Reaction set for ‘closed cycle’ of oxidative pentose phosphate pathway initiated by invertase; (b) reaction
set for ‘closed cycle’ of oxidative pentose phosphate pathway
initiated by sucrose synthase
Table S9 Reaction set for mobilization of chloroplastic
starch and its conversion to sucrose
Table S10 Reaction set for synthesis of storage organ starch
from sucrose
Table S11 Reaction set for synthesis of UDP-glucose from
sucrose
Table S12 Reaction set for synthesis of UDP-glucuronate
from sucrose
Table S13 Reaction set for synthesis of UDP-xylose from
sucrose
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Table S14 Reaction set for synthesis of UDP-arabinose
from sucrose
Table S32 Reaction set for synthesis of proline from sucrose
and NH3
Table S15 Reaction set for synthesis of UDP-galactose
from sucrose
Table S33 Reaction set for synthesis of phenylalanine from
sucrose and NH3
Table S16 Reaction set for synthesis of GDP-mannose
from sucrose
Table S34 Reaction set for synthesis of threonine from
sucrose and NH3
Table S17 Reaction set for synthesis of GDP-fucose from
sucrose
Table S35 Reaction set for synthesis of isoleucine from
sucrose and NH3
Table S18 Reaction set for synthesis of UDP-rhamnose
from sucrose
Table S36 Reaction set for synthesis of tyrosine from
sucrose and NH3
Table S19 Generalized reaction set for polymerization of
NDP-sugars into hemicelluloses and regeneration of NDP
Table S37 Reaction set for synthesis of lysine from sucrose
and NH3
Table S20 Generalized reaction set for polymerization of
NDP-sugars into hemicelluloses, regeneration of NDP and
methylation of sugar residue
Table S38 Reaction set for synthesis of histidine from
sucrose and NH3
Table S21 Reaction set for synthesis of 2-oxoglutarate from
sucrose
Table S22 Reaction set for synthesis of ribose 5-P from
sucrose
Table S23 Reaction set for synthesis of glutamate from
sucrose and NH3
Table S24 Reaction set for synthesis of glutamine from
sucrose and NH3
Table S25 Reaction set for synthesis of alanine from sucrose
and NH3
Table S26 Reaction set for synthesis of arginine from
sucrose and NH3
Table S27 Reaction set for synthesis of aspartic acid from
sucrose and NH3
Table S28 Reaction set for synthesis of asparagine from
sucrose and NH3
Table S29 Reaction set for synthesis of serine from sucrose
and NH3
Table S30 Reaction set for synthesis of cysteine from
sucrose, NH3 and SO4
Table S31 Reaction set for synthesis of glycine from sucrose
and NH3
The Author (2010)
Journal compilation New Phytologist Trust (2010)
Table S39 Reaction set for synthesis of valine from sucrose
and NH3
Table S40 Reaction set for synthesis of leucine from sucrose
and NH3
Table S41 Reaction set for synthesis of methionine from
sucrose, NH3 and SO4
Table S42 Reaction set for synthesis of tryptophan from
sucrose and NH3
Table S43 Reaction set for synthesis of oxaloacetic acid
(OAA) from sucrose
Table S44 Reaction set for synthesis of malic acid from
sucrose
Table S45 Reaction set for synthesis of citric acid from
sucrose
Table S46 Reaction set for synthesis of aconitic acid from
sucrose
Table S47 Quantum requirement and nitrate photoassimilation
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