From sunlight to phytomass: on the potential efficiency of converting solar radiation to phyto-energy



This article is corrected by:

  1. Errata: Corrigendum Volume 208, Issue 4, 1276, Article first published online: 9 October 2015

  • 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.

Author for correspondence:
Jeffrey S. Amthor
Tel: +61 02 8627 1050



III.Solar radiation absorption942
IV.Quantum requirement for CO2 assimilation943
VI.Photosynthate mobilization and translocation948
VIII.Substrate requirement for growth949
IX.From sunlight to phyto-energy: potential overall efficiency953


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 out-put : 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 30°C 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 20°C, the 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 (ΔHC, 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 ΔHC. For example, grain sorghum (Sorghum bicolor) whole-plant ΔHC 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 ΔHC must be considered when comparing solar energy use between the species. Indeed, a wide range of ΔHC 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, ΔHC is infrequently measured in plant production studies.

Table 1.   Selected measured phytomass heats of combustion
SpeciesHeat of combustion (ΔHC, MJ kg−1)Source
RootStem, woodLeafSeed, fruitWhole plant
  1. Glycine max‘root’ included nodules.

  2. 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).

Glycine max18.317.219.022.819.1A
Helianthus annuus16.516.116.028.316.7B
Miscanthus × giganteus16.518.219.0 18.0D
Sorghum bicolor16.717.517.717.017.2A
Zea mays13.417.416.918.017.5C
Juglans regia (seedlings)17.017.719.033.3 E
Hardwood forest trees 17.7–20.418.8–21.0  F
Pinus species–29.8 B, F
Tropical mangrove forest16.917.717.517.0 G
Tropical moist forest16.617.616.118.0 G
Table 2.   Heats of combustion of key phytomass constituents
ConstituentFraction carbonHeat of combustion (ΔHC)
(kg C kg−1)(MJ kg−1)[MJ (mol C)−1]
  1. Details are given in Supporting Information Table S1.

  2. 1, Ranges for arabinose, xylose, fucose, galactose, glucuronate, methylated glucuronate, mannose and rhamnose residues in hemicelluloses.

  3. 2, Ranges for p-coumaryl alcohol, coniferyl alcohol and sinapyl alcohol residues in lignins.

  4. 3, Ranges for the 20 amino acid residues in proteins.

  5. 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.

  6. 5, Ranges for aconitic acid, citric acid, malic acid, oxalic acid and oxaloacetic acid (OAA).

Amino acids30.297–0.65413.91–31.620.400–0.750
Organic acids50.267–0.4142.70–11.410.122–0.332

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 phyto-energy. 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.

Figure 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 (ΔHC) 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.

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, including solar radiation. A new compilation of plant constituent ΔHC 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 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.

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), 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 36.6°N 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).

Figure 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 μmol (photons) m−2 s−1 in this waveband, which results in 4.55 mol photons MJ−1 between 400 and 700 nm.

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.

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.

1. C3 photosynthesis

C3 photosynthesis – from CO2 to fructose 6-P – can be summarized by (Supporting Information Table S2a):


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., 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 pseudo-cyclic 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 ribulose-1,5-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):


where only 10 of the ‘15 O2’ molecules oxygenate ribulose-1,5-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 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):


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):


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 C3plant 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 11°C, 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).

Figure 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 = 2Γ*/Ci is shown, where Γ* 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). Γ* was calculated after Bernacchi et al. (2001): inline imagewhere 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.

Table 3.   Theoretical (minimal) quantum requirements for CO2 assimilation in the absence of respiration
SystemvO/vCC4 overcyclingQuantum requirement (photon/CO2)
H+/ATP = 4H+/ATP = 14/3
  1. 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).


4. C4 photosynthesis

For present purposes, C4 photosynthesis refers to the NADP malic enzyme type, which includes the major C4 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 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 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. 23°C 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 & 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 37°C 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 30°C 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 20°C, 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 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 (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.

Figure 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.

The H+/ATP ratio of mitochondrial ATP synthases was experimentally estimated to be c. two several decades ago 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.

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 hypothetical closed cycle of OPPP (Beevers, 1961) oxidizing sucrose, summarized by (Table S8a):


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).

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):


where (starch)n indicates a starch polymer of n glucose residues. Thus, 2/YATP,sucrose sucrose are respired to mobilize each sucrose unit (starch → 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 (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.

VII. Maintenance

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 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.

VIII. Substrate requirement for growth

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 ΔHC 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).

1. Cellulose

Cellulose consists of long chains of β(1→4)-linked glucose residues and may be nature’s most abundant polymer. 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:


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).

Table 4.   Calculated potential efficiencies of energy use (YE) during the biosynthesis of polysaccharides and lignins from sucrose
Polymer or monomer residueYE (J J−1)
  1. 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 (ΔHC cellulose)/(ΔHC sucrose – ΔHC fructose). For all others, YE is given by (ΔHC residue in polymer)/(ΔHC in sucrose requirement); see Supporting Information Table S1 for ΔHC 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 ΔHC 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.

Starch (storage organ)0.972
Hemicelluloses (residues)
  Glucuronate (methylated)0.802
Lignins (residues)
  p-Coumaryl alcohol0.831
  Coniferyl alcohol0.737
  Sinapyl alcohol0.674

Traditional substrate requirement calculations (e.g. Penning de Vries et al., 1974; Williams et al., 1987) were summarized as:


Together with the traditional estimate of 36 ATP/glucose resulting from respiration, YE would then be 0.95 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).

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), NDP-sugars 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

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 ΔHC 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.

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). ΔHC also varies among proteins. The measured ΔHC 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 ΔHC = 24.5 MJ kg−1.

Table 5.   Calculated potential efficiencies of energy use (YE) during amino acid synthesis from sucrose, NH3 and SO4, and polymerization into protein
Amino acidYE (J J−1)
Amino acid1Polymerized residue1
  1. 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 ΔHC values were from Supporting Information Table S1 (amino acid and amino acid residue ΔHC 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).

  2. 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.

Aspartic acid0.8480.695
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 (ΔHC)
Calculated resultProtein
  1. Whole-protein YE and ΔHC values were calculated by summing the amino acid residue YE values from Table 5 and the ΔHC 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).

  2. 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 α3β3γδε (with δ chain from Sorghum vulgare) and F0 subunits in the ratio ab2c14 (P05022, P00827, P0C1M0, Q07300, P00835, P17344, P48186, P69449).

YE (J J−1)0.7370.7260.7300.7290.7310.7310.7290.7350.733
ΔHC (MJ kg−1)25.3024.4524.5124.5824.4224.7524.1824.1824.60

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.

7. Organic acids

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).

8. Minerals

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 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.

9. Whole plants

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 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.

Table 7.   Calculated potential whole-plant YE and ΔHC of generic C3 and C4 grain crops
Plant constituent or whole plantC3C4
Fraction (kg kg−1)YE (J J−1)ΔHC (MJ kg−1)Fraction (kg kg−1)YE (J J−1)ΔHC (MJ kg−1)
  1. Columns labeled ‘fraction’ specify the contributions of individual constituents (i.e. compounds, classes of compound or minerals) to whole-plant dry mass. Values for whole-plant YE are whole-plant ΔHC divided by ΔHC 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.

Organic acids0.0600.90210.320.0550.90210.32
Whole plant1.0000.86917.641.0000.87917.55

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 ΔHC 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).

IX. From sunlight to phyto-energy: potential overall efficiency

1. Theoretical efficiency

The multiplication of component efficiencies gives whole-plant 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 30°C and 0.053 J J−1 at 20°C (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 30°C) and 0.118 J J−1 (at 20°C), 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 30°C, but, at 20°C, the C3 system could be marginally more efficient. At greater [CO2], the efficiency of the C3 (but not C4) system increases.

Table 8.   Potential solar-energy-use efficiency of generic C3 and C4 grain crops
‘Process’ linking incident total solar irradiance to production of new phyto-energy‘Process’YE (J J−1)
  1. All incident solar radiation was assumed to be intercepted and photosynthesis (minus photorespiration) produced 30% starch and 70% sucrose. Atmospheric [CO2] was 350 ppm.

Photosynthetically active radiation (PAR) fraction of incident total solar radiation0.480.480.48
Canopy absorption of PAR0.930.930.93
Fraction of PAR absorption by photosynthetic pigments0.920.920.92
Photosynthesis (with photorespiration)0.1780.1400.165
Photosynthate mobilization/translocation0.9730.9730.973
Maintenance respiration0.850.850.88
Efficiency of growth0.8690.8690.879
Total (per unit incident total solar radiation)0.05250.04120.0509
Total (per unit absorbed PAR)0.11770.09240.1140

At 30°C, 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 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.

Table 9.   Theoretical (quantum-based) estimates of potential solar-energy-use efficiency
Potential efficiency (J J−1)NotesSource
Incident total solar radiation basisAbsorbed PAR basis
C3 systemC4 systemC3 systemC4 system
  1. 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.

  2. 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 ΔHC 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 ΔHC 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 ΔHC of 17.6 MJ kg−1. (6), At 25°C. The C4 estimate is for vO/vC = 0 and without C4 overcycling. (7), At 30°C. The C4 estimate is for vO/vC = 0 and without C4 overcycling.

  3. 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).

0.053 0.12 (1)A
0.059 0.14 (2)A
0.032 0.068 (4)C
 0.043 0.091(5)D
0.053 0.118 20°CThis review
0.0410.0510.0920.11430°CThis review

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 30°C (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 light-saturated C4 photosynthesis.

How do theoretical estimates of potential solar-energy-use 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 30°C, whereas the last two values exceed the potential calculated for 30°C, but are c. 85% of the theoretical potential at 20°C. These actual C3 crops were grown in atmospheres with slightly lower [CO2] values, and therefore modestly 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 solar-energy-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 ΔHC of c. 18 MJ kg−1, was c. 0.78 J J−1intercepted 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 ΔHC of 17.5 MJ kg−1 (Lieth, 1968), the efficiency was c. 0.078 J J−1 relative to absorbed PAR (again c. 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.

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 solar-energy-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.


Thanks to Don Ort for helpful dialog, Bob Loomis for decades of encouragement, and two anonymous referees for important suggestions.