Annals of Botany 85: 45–54, 2000 Article No. anbo.1999.0996, available online at http:\\www.idealibrary.com on

Modelling the Components of Plant Respiration: Some Guiding Principles

M.G.R.CANNELL* and J.H.M.THORNLEY Institute of Terrestrial Ecology, Bush Estate, Penicuik, Midlothian EH26 0QB, UK

Received: 11 June 1999 Returned for revision: 28 July 1999 Accepted: 20 September 1999

Respiration is poorly represented in whole plant or ecosystem models relative to photosynthesis. This paper reviews the principles underlying the development of a more mechanistic approach to modelling plant respiration and the criteria by which model behaviour might be judged. The main conclusions are as follows: (1) Models should separate C substrate from structure so that direct or indirect C substrate dependence of the components of respiration can be represented. (2) Account should be taken of the fact that some of the energy for leaf respiration is drawn from the light reactions of photosynthesis. (3) It is possible to estimate respiration associated with growth, nitrate reduction, symbiotic N# fixation, N-uptake, other ion uptake and phloem loading, because reasonable estimates are available of average specific unit respiratory costs and the rates of these processes can be quantified. (4) At present, it is less easy to estimate respiration associated with protein turnover, maintenance of cell ion concentrations and gradients and all forms of respiration involving the alternative pathway and futile cycles. (5) The growth-maintenance paradigm is valuable but ‘maintenance’ is an approximate concept and there is no rigorous division between growth and maintenance energy-requiring processes. (6) An alternative ‘process-residual’ approach would be to estimate explicitly respiratory fluxes associated with the six processes listed in (3) above and treat the remainder as a residual with a phenomenological ‘residual maintenance’ coefficient. (7) Maintenance or ‘residual maintenance’ respiration rates are often more closely related to tissue N content than biomass, volume or surface area. (8) Respiratory fluxes associated with different processes vary independently, seasonally and during plant development, and so should be represented separately if possible. (9) An unforced outcome of mechanistic models should be a constrained, but non-constant, ratio between whole plant gross photosynthesis and respiration. # 2000 Annals of Botany Company

Key words: Respiration, photosynthesis, growth, maintenance, substrate, N uptake, nitrate reduction, symbiotic N# fixation, phloem loading, model.

underlying mechanisms. Respiration is a very large flux; it INTRODUCTION is intimately linked to many other processes—growth, The need to predict the effect of climate change is promoting allocation, nitrogen uptake etc.—and is important in a critical re-examination of ecosystem models, which are determining net primary production and plant death. Broad- ultimately the only tools we have to forecast the effect of brush approaches, which ignore mechanisms, may make it gradual change over decadal timescales. Empirical or more impossible to detect and evaluate a range of possible mechanistic models of photosynthesis enable gross photo- responses and may fail to predict important effects. synthesis to be predicted with some confidence (e.g. Second, there have recently been some theoretical and Farquhar et al., 1980; Cannell and Thornley, 1998). But experimental advances in understanding respiration, e.g. by having estimated assimilate production quite accurately, Ryan and coworkers (Ryan, 1991, 1995; Ryan et al., 1996a, most models then dispense with about half of the assimilate 1997), Bouma and coworkers (Bouma, 1995; Bouma et al., in respiration and allocate the remainder for the growth 1995; 1996) and Gifford (1994, 1995). There is now of plant parts using somewhat arbitrary coefficients or sufficient new information to justify a re-evaluation of the proportions based on widely-ranging observed values (e.g. old concept of growth and maintenance respiration A/ gren et al., 1991; Ryan et al., 1996b). In the most (McCree, 1970; Thornley, 1970) developed by Thornley extreme case, respiration is simply subtracted as a fixed (1977), subsequently extended to include ion uptake by fraction of gross photosynthesis (Coops et al., 1998; Johnson (1983, 1990) and still almost universally adopted as Waring et al., 1998). the paradigm for representing respiration in models This, and the following paper (Thornley and Cannell, (Amthor, 1994, gives an excellent modern statement of this 2000), re-examines the principles and practice of modelling paradigm). plant respiration, with the following two convictions. First, In this paper, we use the recent literature on plant confidence in predicting future ecosystem responses, as respiration to highlight some of the principles that need to opposed to describing past data, may be improved by be considered when developing more mechanistic representing respiration, at least partially, in terms of approaches to plant respiration. We also identify some of the essential observations that models must be capable of simulating. This account draws information from * For correspondence. Fax j44(0)1314453943, e-mail mgrc! recent reviews of respiration, which offer more compre- ite.ac.uk hensive descriptions of the literature (Lambers et al., 0305-7364\00\010045j10 $35.00\0 # 2000 Annals of Botany Company 46 Cannell and Thornley—Modelling the Components of Plant Respiration 1983; Amthor, 1984, 1986, 1991, 1994; Farrar, 1985; uptake and protein resynthesis). Consequently, we should Ryan, 1991; Poorter and Villar, 1997; Reich et al., 1998a, expect the overall demand for ATP and NAD(P)H and b). The companion paper (Thornley and Cannell, 2000) hence the respiration rate to be positively correlated with then re-examines how respiration is represented in models the supply rate and\or concentration of C substrates in and how it may be represented more mechanistically, taking the plant (Farrar, 1985, pp. 432–433; Amthor, 1994, into account the principles outlined below. pp. 508–509). A brief discussion of our assumptions regarding glucose dissimilation, ATP and NADPH production and the P\O RESPIRATION IS CONTROLLED BY BOTH ratio is given in the Appendix. ENERGY DEMAND AND THE SUPPLY OF C SUBSTRATES RESPIRATORY COSTS IN LEAVES MAY BE LESS THAN EXPECTED FROM THEIR MASS Mitochondrial respiration consumes C substrates (mostly OR N CONTENT glucose) to provide energy (ATP) and reducing power (NAD(P)H) for all energy-requiring processes in plants. Figure 1 shows that ATP and NAD(P)H can also be drawn Figure 1 presents a simplified scheme of the way in which directly from the light reaction of photosynthesis. This C substrates are used to generate ATP and NAD(P)H in occurs in chloroplasts during the day when there is excess support of growth and other processes. ATP production and can supply at least part of the energy Assuming that the enzymes involved in respiration are required for growth, protein turnover and phloem loading present in excess, rates of respiration may be viewed as in leaves without consuming C substrates (Raven, 1976; being co-limited by the rate of supply of C substrates (source Lawlor, 1987). In effect, excess energy in the chloroplasts is or ‘push’ limited) and by the demand for ATP and used directly to support respiration, avoiding the need to NAD(P)H by energy-requiring processes, reflected in the synthesize sugars and then respire them. Also, during the rate of supply of ADP and NAD(P) (sink or ‘pull’ limited) night, photosynthetic proteins are not activated, so it is (Farrar, 1985; Amthor, 1994). In growing plants, the rates likely that less ATP is required for protein maintenance. of most processes requiring ATP or NAD(P)H are them- Thus, the consumption of C substrates for respiration in selves dependent on the rate of supply of C substrates either leaves may be less than expected from their mass or N directly (growth and phloem loading) or indirectly (ion content. Allowance should be made for this in models, e.g.

Photosynthesis

C substrate (glucose) CO C skeletons 2 (glucose) Respiration for growth

Direct (Photosynthesis) ADP ATP growth NAD(P), Pi NAD(P)H resp- iration

Nitrate reduction (G) N fixation (G) N uptake (G, M) Other ion uptake (G, M) Phloem loading (G, M) Protein (macromolecular) resynthesis (M) Cell ion concs/gradients (M) Alternative pathway, futile cycles (W)

Plant tissue Litter (cellulose)

F. 1. Simplified scheme of the carbon biochemistry of growth and respiration. Arrows indicate fluxes. G, Growth; M, maintenance; W, wastage respiration. Cannell and Thornley—Modelling the Components of Plant Respiration 47 by adjusting foliage growth and maintenance respiration Thornley and Johnson, 1990, p. 352). For most vegetative n coefficients according to current photosynthetic activity. plant tissue, the growth yield YG is in the range 0 7to 0n85 (this is taking account of the direct construction cost only) equivalent to construction costs or glucose require- PROCESSES WITH QUANTIFIABLE ments in the range 1n2to1n4 g glucose (g dry matter)−" n n RESPIRATORY FLUXES: GROWTH, and CO# production coefficients in the range 0 2to04g −" NITRATE REDUCTION, N# FIXATION, CO# (g dry matter) . N UPTAKE, OTHER ION UPTAKE AND For the construction of organic acids with their low n PHLOEM LOADING energy content (high oxidation state), YG can range from 1 0 to 2n4 g C in organic acid product per g C in glucose At least nine plant processes can be separated which require n energy: growth (Penning de Vries et al., 1983; Thornley substrate, with a value of 1 4 for malate. Equivalent values and Johnson, 1990); nitrate reduction, symbiotic dinitrogen of YG, in units of g C in product per g C in glucose substrate are 0n85 to 1n0 for carbohydrates, 0n8to0n85 for lignins, 0n7 fixation (Simpson, 1987); root N-uptake (Bloom et al., n n 1992); other ion uptake (Thornley and Johnson, 1990, p. for lipids (palmitate), and 0 5to08 for proteins and nucleic 348); phloem loading (Geiger, 1975; Bouma, 1995), protein acids, depending on whether the nitrogen source is ammo- turnover (Vierstra, 1993); maintenance of cell ion con- nium or nitrate. Despite this range, the overall construction centrations and gradients (Bouma, 1995); and apparently cost of vegetative plant biomass is surprisingly constant. Many experimental estimates of an overall YG give a figure wasteful, heat-producing respiration following the alter- n native (cyanide resistant) pathway or futile cycles (Hue, of about 0 7 g C in product tissue per g C in glucose 1982; Lambers, 1985). In this analysis we do not attempt substrate, differing by 10% or less on average between plant to separate out respiration associated with secondary meta- parts, woody and herbaceous species, fast and slow-growing bolism, detoxification of pollutants or all forms of damage species and growth conditions, because of covariation repair. between the classes of constituents in plant biomass (Poorter For each energy-requiring process it is theoretically and Villar, 1997). However, in plant growth simulators, possible to define the respiratory cost (in terms of C where some of the growth costs may be separately accounted for (e.g. nitrate reduction, phloem loading and N uptake), it substrate consumed, CO# emitted or O# consumed) per unit n is preferable to use higher values of YG, in the range 0 75 to of process—the specific unit cost. Respiration rate is then n given by: 0 85, because this now applies more specifically to the direct biochemical costs of synthesis. Thus, the value(s) for YG respiration rate l specific unit costirate of the process used in models depend on how other components of (1) respiration are represented. It is necessary to determine both specific unit cost and the rate of the process in order to calculate the contribution to Nitrate reduction respiration. Specific unit respiratory costs can be approxi- mately quantifiable for six of the nine processes: growth, The full cost of nitrate reduction is 8 mol H (mol N)−" nitrate reduction, N# fixation, N-uptake, other ion uptake (e.g. Marschner, 1995, p232), giving rise to a glucose C and phloem loading. The rates of five of these six processes requirement for respiration of (8i6i12\24)\14 l 1n72 kg can also be reasonably quantified. For ‘other ion uptake’ C (kg nitrate N reduced to ammonia)−", assuming that the flux is quantifiable, but, because of uncertainties glucose with 6 C atoms of relative molecular mass 12 is concerning ion leakage and exudation, the gross flux may be equivalent to 24H. substantially larger than the net flux.

Symbiotic N# fixation Growth respiration Symbiotic N# fixation requires a minimum of 16 ATP and Growth respiration is defined here in terms of ‘growth 4 NADPH per mol N# fixed (Simpson, 1987; Thornley and yield’, YG, the units of C appearing in new biomass per unit Johnson, 1990, p. 321) implying a minimum glucose C of glucose C utilized for growth (Thornley, 1970; called requirement for respiration of 2 kg C (kg dinitrogen N −" ‘growth efficiency’ by Yamaguchi, 1978, although YG is not reduced to ammonia) , although some of the energy in the a true efficiency). The ‘construction cost’ or ‘glucose hydrogen evolved may be recovered and there are costs in requirement’ in units of C of a glucose substrate required synthesizing and maintaining a functional rhizobial popu- \ per C unit of new biomass is 1 YG (Penning de Vries et al., lation. Thus, theoretically, dinitrogen fixation is only slightly 1983) and the ‘growth coefficient’ in units of C respired per more expensive than the full costs of nitrate reduction, in C unit of new biomass synthesized from a glucose substrate the ratio of 2:1n72. In practice, however, measured costs of k \ is given by (1 YG) YG (this is more accurately described as N# fixation are generally higher than minimum values. In −" a‘CO# production coefficient’). units of kg C (kg dinitrogen fixed) , measured values n n The parameter YG can be estimated from experimental averaged 6 5 in the work of Ryle et al. (1979), 5 7in data e.g. by using a regression method (see Thornley, 1970) the review by Phillips (1980) and 3n1 in the review by Sheehy or calculated theoretically from the chemical composition (1987, derived from his Fig. 7). Values in the range 4–6 kg of new plant material (Penning de Vries et al., 1974; C (kg dinitrogen fixed)−" seem most acceptable. 48 Cannell and Thornley—Modelling the Components of Plant Respiration derived from gross structural mass times the non-N mineral N uptake concentration (about 4%, but in reality variable) less an Bouma et al. (1996) obtained a theoretical specific cost for amount recovered from senescing plant parts. n − −" nitrate ion uptake of 0 43 mol O# (mol NO$ ) , assuming the ions crossed only one membrane, that 2 mols of H+ were − + Phloem loading required per mol NO$ , 1 mol H was pumped over a membrane by the hydrolysis of one ATP to ADP and The respiratory costs of phloem loading, including all \ oxidative phosphorylation (P O#) had an efficiency of pathways from starch in the chloroplast to apoplastic n −" n l \ n 4 7 mol ATP (mol O#) (0 43 2 4 7). loading of sucrose into the phloem lie, theoretically, in the + n n −" The cost of ammonium (NH% ) ion uptake may be similar range 2 4–4 0 mol ATP (mol sucrose) , equivalent to + + n n −" to that of potassium (K ), which requires 1 mol H per mol 0 5–0 8 mol CO# (mol sucrose) (assuming 1 CO# is + cation (e.g. Marschner, 1995, chapter 2). Thus, NH% may equivalent to 5 ATP) agreeing well with measured values of − n −" be half as costly to take up as NO$ . However, this is an about 0 7 mol CO# (mol sucrose) (Bouma et al., 1995). approximation, because there are strong interactions be- This is equivalent to 0n7\12 l 0n06 kg C respired from a + + −" tween K and NH% uptake. Also, because of pH effects, glucose substrate (kg C in sucrose loaded) . Phloem − + combinations of NO$ and NH% may be especially favoured unloading is assumed to occur passively through the + energetically, uptake of NH% alone may cause the plant pH symplast and have no respiratory cost (Ho, 1988). problems, incurring other respiratory costs. Finally, there is the possibility that NH + may be deprotonated outside the % PROCESSES WITH LESS-QUANTIFIABLE membrane, which it can then enter and cross without RESPIRATORY FLUXES: PROTEIN assistance. TURNOVER, CELL ION CONCENTRATION Measured uptake is the difference between ion influx and MAINTENANCE AND WASTAGE ion efflux. One explanation for variation in observed costs of net uptake is variation in efflux, as well as the inclusion Although there is no clear distinction between quantifiable of some costs of maintaining cell ion gradients. Bouma et al. and non-quantifiable respiration fluxes, we suggest that, at n − −" (1996)’s theoretical estimate of 0 43 mol O# (mol NO$ ) is, present, it is less easy to estimate the specific unit respiratory however, consistent with experimental estimates in the costs and\or the rates of the remaining three energy- n n − −" range 0 39–0 67 mol O# (mol NO$ ) . Previous experimental requiring processes: protein turnover, maintenance of cell n n − −" estimates were higher [0 83–1 16 mol O# (mol NO$ ) ; Veen, ion concentration and gradients and all forms of wastage 1980; Van der Werf et al., 1988] as have been more recent respiration. estimates, which suggest that costs are greater for slow- n n growing species [Scheurwater et al., 1998; 0 41–1 22 mol O# Š − −" Protein turno er (mol NO$ ) ]. In this study, we assume that the respiratory cost for the The orderly degradation and resynthesis of proteins is − l − n uptake of 14 g NO$ N 1 mol NO$ Nis05 mol O# or required for acclimation and development and to enable N 2 mol H+ or 2 mol ATP l 2i6\30 l 2\5 mol C in glucose to be used efficiently (Vierstra, 1993). The respiratory costs respired (assuming 1 mol glucose, C'H"#O', respired yields can, in theory, be calculated from the specific energy costs 30 mol ATP) l 12i2\5 g glucose C respired. Therefore, in of forming peptide bonds and the degradation constant for − \ i \ l −" mass units, the cost of NO$ uptake is (2 5) (12 14) protein turnover (s ), knowing the amount of N in the n − + n 0 34 g glucose C respired per g NO$ N. For NH% uptake, tissue and assuming 1 26 mol N-protein (mol peptide n + −" we use 0 17 g glucose C respired per g NH% N taken up. We bond) (Bouma et al., 1996). The problem is that both the n recognize that the assumption that 0 5 mol O# is used in energy costs of forming peptide bonds and the degradation − \ uptake respiration per mol NO$ and that the P O# ratio constant can vary by at least a factor of two (De Visser is 5 (cf. 4n7 estimated by Bouma et al., 1996), with the et al., 1992; Van der Werf et al., 1992). Thus, in practice, respiration of 1 mol glucose providing 30 ATP (based on there may be no advantage in using eqn (1) to estimate coupled mitochondrial respiration) are all debatable. this component of respiration.

Uptake of other ions Maintaining cell ion concentrations and gradients The respiratory cost of the uptake and transport of ions In order to maintain a near-constant environment in the other than N (P, K, Ca, Mg etc.) has been assumed by cytosol, cells need to take up ions to counter ion effluxes or Thornley and Johnson (1990, p. 348) to be 1 H+ or 1 ATP other losses. The respiratory cost of maintaining cell ion per ion, equivalent (see above calculation) to (1i6\30 l concentrations and gradients can, in theory, be calculated 1\5)i(12\40) l 0n06 g glucose C respired per g mineral from the rate of efflux of ions and a specific cost which taken up. This assumes that the mineral relative molecular depends on the number of active membrane passages of the mass is 40 and constant—ignoring the fact that, in reality, ions and the proton-ion and proton-ATP stoichiometries the average molecular weight of minerals taken up will (Bouma, 1995, p. 81). However, in practice, there is too little vary. information on ion gradients in cell and respiratory Whereas for N, the amount taken up can be modelled pathways to quantify these components in complex multi- explicitly, the uptake of other minerals may simply be cellular tissues of plants, and, in experimental estimates of Cannell and Thornley—Modelling the Components of Plant Respiration 49 respiration, this component is commonly confounded with represented, and the maintenance coefficients must be the costs of protein turnover in leaves and stems, or with net regarded as empirical devices with no very rigorous meaning. ion uptake in roots. Maintenance coefficient values differ between leaves, stems and roots, because different processes are included, and AlternatiŠe pathway respiration and futile cycles some parameter adjustment is normally necessary to give realistic model performance. Plant mitochondria possess mechanisms which can oxidize surplus NADH without generating ATP. This is similar to wastage respiration produced by futile cycles (Hue, 1982). Process-residual approach Also, the hydrolysis of ATP may not be coupled to energy An alternative approach is to calculate the respiratory requiring processes. The fraction of C substrate that is used costs separately for growth in each plant part (perhaps then this way is highly variable among tissues, but tends to be better called ‘local’ growth respiration), nitrate reduction, greatest when there are high concentrations of respiratory N# fixation, N uptake, other ion uptake and phloem substrates, leading to the hypothesis that it represents a loading (the six quantifiable processes) and regard the kind of energy overflow (Lambers, 1997). Although unit remainder as a residual. Residual respiration is then respiratory costs could be specified, it is currently impossible associated with protein turnover, maintaining cell ion to specify the rate of this component of respiration. concentrations\gradients and includes all wastage respir- ation (and any unidentified components). This residual may DIFFERENT WAYS OF CLASSIFYING THE be estimated, like maintenance respiration, by selecting an COMPONENT ENERGY REQUIRING appropriate coefficient, which may be termed the ‘residual PROCESSES maintenance’ coefficient and may differ between plant Growth-maintenance paradigm parts. The advantages of this approach are that (1) the fraction The nine processes considered above are normally grouped of total plant respiration which has to be estimated using an together into those associated with ‘growth’ and those empirical coefficient is reduced to a minimum, reducing associated with ‘maintenance’. The growth-maintenance uncertainty in the overall estimate of respiration, and (2) paradigm may be acceptable and useful for some purposes, information is gained on the energy costs of different but it should be realized that there is no rigorous division processes, which differ from each other and can vary among between growth and maintenance energy-requiring pro- species (Lambers and Poorter, 1992; Bryla et al., 1997; cesses (Table 1). Ion uptake and phloem loading have Eamus and Prichard, 1998). The disadvantage, of course, elements of both growth and maintenance and all forms of is that many parameters have to be defined for the dif- wastage respiration are neither. Also, maintenance is ferent processes, some of which are uncertain, as discussed incomplete in mature plants, because there is some retrieval above. of energy and substrates from senescing tissues, possibly leading to overestimation of maintenance costs. Addition- MAINTENANCE OR ‘RESIDUAL ally, growth respiration normally includes the cost of nitrate MAINTENANCE’ RESPIRATION MAY BE A reductions, but it could exclude both nitrate reduction and LESS VARIABLE FUNCTION OF TISSUE N uptake respiration if these were accounted for separately N CONTENT THAN OF BIOMASS (Johnson, 1990). Consequently, when using the growth-maintenance Since a rigorous definition of maintenance respiration is paradigm, the value of YG has to be chosen somewhat elusive, it is hardly surprising that it is difficult to measure pragmatically, depending on how the other processes are a maintenance coefficient unambiguously. Nevertheless,

T 1. Different definitions and classifications of energy-requiring processes in plants

Processes associated Classical growth Processes with growth (G), (G) and represented maintenance (M) maintenance (PR) and and waste (W) (M) paradigm residual approach

Energy requiring processes G M W G M PR Residual

Local growth * * * Nitrate reduction * * * N# fixation * * * N uptake * * * * Other ion uptake * * * * Phloem loading * * * * Protein turnover * * * Cell ion concs\gradients * * * Alternative\futile * * *

This list excludes respiration associated with secondary metabolism, detoxification of pollutants and all forms of damage repair. 50 Cannell and Thornley—Modelling the Components of Plant Respiration some useful tabulations are given by Penning de Vries times taken as approximately unity, averaged over a (1975, table 3), Amthor (1984, table 1) and Amthor (1986, season (Sprugel, 1990; Amthor, 1994). However, main- table A.1) on a mass loss per unit mass per day basis. Values tenance respiration was estimated to represent 79% of the vary greatly with tissue type, with some typical values being annual above-ground respiration in 13-year-old Chamae- 10−' d−" for seeds, 10−% d−" for stem wood, and up to 0n05 d−" cyparis trees in the field in Japan (Paembonan et al., for leaves and roots. There is also considerable variation 1992). with tissue age and growing conditions. In reality, the activities of meristems and proportions of Many studies, based on the growth-maintenance para- meristematic and non-meristematic tissues change during a digm, show that maintenance respiration rates of leaves, season and during the lifetime of plants, especially trees. stems and roots are more closely related to their Kjeldahl N Similarly, the rates of individual energy-requiring processes, contents than to their masses, volumes or surface areas such as ion uptake, N# fixation and phloem loading, change (Ryan, 1991, 1995; Ryan et al., 1996a; Pregitzer et al., 1998) seasonally and during plant development and also differ suggesting that maintenance respiration is directly or among species and environments. One clear advantage of indirectly related to tissue protein content (McCree, 1974; the process-residual approach is that these changes and Penning de Vries, 1975; Thornley, 1982; De Visser et al., differences are revealed. 1992). However, in one notable study, maintenance respiration was poorly related to leaf N content (e.g. Byrd et al., 1992). Also, maintenance respiration rates per unit N vary among species, tissue types and with growth rate, RATIOS BETWEEN RESPIRATION AND presumably because only part of this lumped respiration GROSS PHOTOSYNTHESIS ARE term is directly related to protein content, and, in any case, CONSERVATIVE BUT VARIABLE the proportionalities between tissue N content, protein content and respiratory function are variable (see Ryan, Because photosynthesis provides the substrate for res- 1991; Amthor, 1994). For instance, there is a 65% difference piration and associated processes, there is a close coupling in the relationship between plant N content and maintenance between the amount of C assimilated and that lost by respiration reported by Irving and Silsbury (1987) and Ryan respiration, so that the ratio of photosynthesis to respiration (1991) and a three-fold difference in the rate of leaf dark is fairly stable when averaged over weeks or longer (Charles- respiration per unit N measured by Jones et al. (1978) and Edwards, 1982, pp. 73–76; Dewar, et al., 1998). Ryan (1995)" (see also Amthor, 1994; Reich et al., 1996, There is a substantial literature supporting the classic 1998a, b). observations of McCree and Troughton (1966) that the Thus, in practice, coefficients of maintenance respiration carbon use efficiency (CUE: net primary productivity per per unit N content have to be chosen with a measured range unit of C assimilated by photosynthesis) of plants varies based on the emergent behaviour of the model. This within a restricted range (normally 0n4–0n6) over a wide range pragmatism applies equally to ‘residual maintenance’ as to of plant size and environmental conditions. Notable recent maintenance in the growth-maintenance paradigm. studies showing limited variation in CUE are those of: (1) Gifford (1994, 1995) on wheat, over two orders of magnitude in biomass, a range of temperatures and CO RESPIRATORY FLUXES ASSOCIATED # concentrations; (2) Monje and Bugbee (1998) over the WITH DIFFERENT PROCESSES VARY vegetative life of wheat; (3) Ziska and Bunce (1998) on INDEPENDENTLY soybean over a range of temperatures; (4) Ryan et al., As a rule-of-thumb, the ratio of growth to maintenance (1996a)onPinus radiata with extreme irrigation and respiration in the growth-maintenance paradigm is some- fertilizer treatments; (5) Goetz and Prince (1998) on Populus deltoides and Picea mariana over two orders of magnitude in biomass; and (6) Reich et al. (1998a, b) on trees and other plants, showing close couplings between measured photo- synthesis and respiration. " Ryan’s (1995, his Fig. 3) value for tree foliage was 2n62 µmol C However, it is also clear that CUE is not constant. Models −" −" m respired (mol Kjeldahl N) s at 10 C. This converts to a rounded which assume constancy may overlook important variation 20 mC value of 0n6 kg C respired (kg N)−" d−" [multiply by 10−'i86400 s d−"i0n012 kg C mol−" (0n014 kg N mol−")−"i0n35−"]. (Coops et al., 1998; Waring et al., 1998). Ryan et al. The last item of 0n35 is a consequence of the temperature function (1977) found CUE values from 0n36 to 0n68 in Pinus used by Thornley (1988, Fig. 3.6). Ryan’s measurements of gas stands in different environments, and conifers seem to exchange were made at night over a 4 h period (2300–0300 h) on fully have substantially smaller CUEs than broadleaved tree et al expanded foliage. Jones . (1978), working with perennial ryegrass, species, perhaps owing to their larger foliage biomass (Goetz extended the period of darkness to 46 h, and assumed that the CO# efflux between 40 and 46 h represented ‘maintenance’ respiration. and Prince, 1998). In some circumstances, respiratory costs They analysed the CO efflux over 48 h of darkness. Protein content can be appreciably less at low temperatures and in high # − was determined by a Kjeldahl determination of N less NO$ N mul- CO (see Amthor, 1991, 1994). Also, respiration is likely n −" −" # tiplied by 6 25. Their mean value of 85 mg CO# (g protein) d at to change as a fraction of C fixation in plants with varying 15 mC converts to a rounded 20 mC value of 0n2 kg C respired −" −" −' −"i −" C storage and may exceed C fixation in plants that are (kg N) d [multiply by 10 kg mg 12 kg C (44 kg CO#) i6n25 g protein (g N)−"i1000 gN (kg N)−"i0n7−"]. drying. Cannell and Thornley—Modelling the Components of Plant Respiration 51 trations and gradients and all forms of wastage CONCLUSIONS REGARDING MODELLING respiration. The principles and facts outlined above provide guidance on (5) The growth-maintenance paradigm is valuable, but (1) the ways in which respiration may be modelled and (2) there is no rigorous division between growth and some criteria by which model behaviour might be evaluated. maintenance energy-requiring processes, maintenance The main conclusions are summarized below. is an approximate concept, and values of the ‘growth yield’ have to be chosen pragmatically, depending on what is included and how other respiratory processes are represented. Model features (6) An alternative ‘process-residual’ approach is to (1) Respiration requires C substrate and is therefore estimate explicitly respiratory fluxes associated with \ directly and or indirectly C substrate dependent, growth, nitrate reduction, symbiotic N# fixation, N- although it may be stimulated by ADP production uptake, other ion uptake and phloem loading, and (Amthor, 1994). Thus, in order to be mechanistic and treat all other respiration (associated with protein realistic, models should separate C substrate from turnover, cell ion concentration and gradient main- structure so that this dependence can be represented tenance and wastage) as a residual, represented by an (remembering that the substrate-structure separation adjustable phenomenological coefficient. This residual is itself an approximation). Similar arguments apply may be termed ‘residual maintenance’ respiration. to modelling growth and allocation (Cannell and (7) There is considerable empirical evidence that main- Dewar, 1994; Thornley, 1997). tenance (and presumably ‘residual maintenance’) (2) Account should be taken of the fact that respiration respiration may be less variable when expressed as a in leaves may make a smaller demand on C substrates function of tissue N content rather than of biomass, than expected from their mass and N content, owing volume or surface area. to the ATP and NAD(P)H supplied by the light reactions of photosynthesis and the non-activation of Model performance photosynthetic proteins at night. In practice this may be done using an arbitrary reduction factor, as (1) Respiration rates associated with individual processes mechanistic modelling could require explicit rep- are variable individually and in relation to each other resentation of ATP and NAD(P)H pools, photo- during plant development and seasonally. Clearly, it synthetic dark reactions and time steps of a minute or can be valuable for models to simulate and predict less. this variation in order to gain insight and under- (3) It is possible and desirable to distinguish respiration standing. associated with growth, nitrate reduction, symbiotic (2) However, ratios between rates of gross photosynthesis N# fixation, N-uptake, other ion uptake and phloem and respiration—and hence the ratio of net to gross loading, because reasonable estimates can be made of primary production—vary within a limited range the specific unit respiratory costs and the rates of when averaged over weeks or longer, because of the these processes [eqn (1)]. Growth respiration is easily coupling between respiration and C substrate supply. modelled. A reasonable average direct ‘growth yield’ This behaviour should be the unforced outcome of n (YG) of plant vegetative tissues is about 0 8g C mechanistic models (Thornley and Cannell, 1996; appearing in new biomass per g of C substrate Thornley, 1998) but can, of course, also be used to utilized. Values of the specific unit respiratory costs of model the long-term growth of vegetation in a other processes are less certain, but, based on the descriptive manner without insight or explanation earlier discussion, estimates are: for nitrate reduction, (Waring et al., 1998). 1n7 kg C respired from a glucose substrate (kg nitrate −" N) but remembering that this value may be greatly ACKNOWLEDGEMENTS decreased if reduction takes place in the foliage; for symbiotic N# fixation, 4–6 kg C respired from a This work has been supported by the European Union EU- glucose substrate (kg dinitrogen N reduced to am- MEGARICH project. We thank an anonymous referee for monia)−"; for N uptake, 0n34 kg C respired from a suggesting many improvements to the original manuscript. glucose substrate (kg nitrate N)−" and half this for ammonium N uptake; for the uptake of other ions, LITERATURE CITED n 0 06 kg C is respired from a glucose substrate per kg / mineral taken up, and it is assumed that up to 50% of Agren GI, McMurtrie RE, Parton WJ, Pastor J, Shugart HH. 1991. State-of-the-art models of production-decomposition linkages in the minerals in senescing material can be recycled if it conifer and grassland ecosystems. Ecological Applications 1: is required for new growth; and for phloem loading, 118–138. 0n06 kg C is respired from a glucose substrate (kg C Amthor JS. 1984. The role of maintenance respiration in plant growth. loaded)−". Plant, Cell and EnŠironment 7: 561–569. (4) At present, it is less easy to estimate accurately the Amthor JS. 1986. Evolution and applicability of a whole plant respiration model. Journal of Theoretical Biology 122: 473–490. specific unit respiratory costs and\or the rates of Amthor JS. 1991. Respiration in a future, higher-CO# world. Plant, protein turnover, maintenance of cell ion concen- Cell and EnŠironment 14: 13–20. 52 Cannell and Thornley—Modelling the Components of Plant Respiration

Amthor JS. 1994. Plant respiratory responses to the environment and Hue L. 1982. Futile cycles and regulation of metabolism. In: Sies H, their effects on the carbon balance. In: Wilkinson RE, ed. Plant- ed. Metabolic compartmentation. New York: Academic Press, enŠironment interactions. New York: Decker, 501–554. 71–97. Bloom AJ, Sukrapanna SS, Warner RL. 1992. Root respiration Irving DE, Silsbury JH. 1987. A comparison of the rate of maintenance associated with ammonium and nitrate absorption by barley. respiration in some crop legumes and tobacco determined by three Plant Physiology 99: 1294–1301. methods. Annals of Botany 59: 257–264. Bouma TJ. 1995. Utilization of respiratory energy in higher plants. Johnson IR. 1983. Nitrate uptake and respiration in roots and shoots: Requirements for ‘maintenance’ and transport processes. PhD a model. Physiologia Plantarum 58: 145–147. Thesis, Department of Theoretical Production Ecology, Johnson IR. 1990. Plant respiration in relation to growth, maintenance, Wageningen Agricultural University, Wageningen, Netherlands. ion uptake and nitrogen assimilation. Plant, Cell and EnŠironment Bouma TJ, Broekhuysen AGM, Veen BW. 1996. Analysis of root 13: 319–328. respiration of Solanum tuberosum as related to growth, ion uptake Jones MB, Leafe EL, Styles W, Collett B. 1978. Pattern of respiration and maintenance of biomass. Plant Physiology and Biochemistry of perennial ryegrass in the field. Annals of Botany 42: 693–703. 34: 795–806. Lambers H. 1997. Respiration and the alternative pathway. In: Foyer Bouma TJ, de Visser R, van Leeuwen PH, de Kock MJ, Lambers H. CH, Quick P, eds. A molecular approach to primary metabolism in 1995. The respiratory energy requirements involved in nocturnal plants. London: Taylor and Francis, 295–309. carbohydrate export from starch-storing mature source leaves and Lambers H, Poorter H. 1992. Inherent variation in growth rate between their contribution to leaf dark respiration. Journal of Experimental higher plants: a search for physiological causes and ecological Botany 46: 1185–1194. consequences. AdŠances in Ecological Research 23: 187–261. Bryla D, Bouma TJ, Eissenstat DM. 1997. Root respiration in citrus Lambers H, Szaniawski RK, de Visser R. 1983. Respiration for growth, acclimates to temperature and slows during drought. Plant, Cell and EnŠironment 20: 1411–1420. maintenance and ion uptake. An evaluation of concepts, methods, Byrd GT, Sage RF, Brown RH. 1992. A comparison of dark respiration values and their significance. Physiologia Plantarum 58: 556–563. between C3 and C4 plants. Plant Physiology 100: 191–198. Lambers H, Scheurwater I, Mata C, Nagel OW. 1998. Root respiration Cannell MGR, Dewar RC. 1994. Carbon allocation in trees: a review of of fast and slow growing plants, as dependent on genotype and concepts for modelling. AdŠances in Ecological Research 225: nitrogen supply: a major clue to the functioning of slow-growing 59–104. plants. In: Lambers H, Poorter H, Van Vuuren MMI, eds. Inherent Šariation in plant growth. Physiological mechanisms and Cannell MGR, Thornley JHM. 1998. Temperature and CO# responses of leaf and canopy photosynthesis: a clarification using the non- ecological consequences. Leiden: Backhuys. rectangular hyperbola model of photosynthesis. Annals of Botany Lawlor DW. 1987. Photosynthesis: metabolism, control and physiology. 82: 883–892. Harlow, Essex, UK: Longman. Charles-Edwards DA. 1982. Physiological determinants of crop growth. Marschner H. 1995. Mineral nutrition of higher plants. London: London and New York: Academic Press. Academic Press. Coops NC, Waring RH, Landsberg JJ. 1998. Assessing forest McCree KJ. 1970. An equation for the respiration of white clover productivity in Australia and New Zealand using a physiologically- plants grown under controlled conditions. In: Setlik I, ed. based model driven with averaged monthly weather data and Prediction and measurement of photosynthetic productiŠity. satellite-derived estimates of canopy photosynthetic capacity. Wageningen: Pudoc, 221–229. Forest Ecology and Management 104: 113–127. McCree KJ. 1974. Equations for the rate of dark respiration of white De Visser R, Spitters CJT, Bouma TJ. 1992. Energy costs of protein clover and grain sorghum as functions of dry weight, photo- turnover: theoretical calculation and experimental estimation synthetic rate and temperature. Crop Science 14: 509–514. from regression of respiration on protein concentration of full- McCree KJ, Troughton JH. 1966. Non-existence of an optimum leaf grown leaves. In: Lambers H, Van der Plas LHW, eds. Molecular, area index for the production rate of white clover grown under biochemical and physiological aspects of plant respiration. The constant conditions. Plant Physiology 41: 1615–1622. Hague: Academic Publishing. Monje O, Bugbee B. 1998. Adaptation to high CO# concentration in an Dewar RC, Medlyn BE, McMurtrie RE. 1998. A mechanistic analysis optimal environment: radiation capture, canopy quantum yield Š of light and carbon use efficiencies. Plant, Cell and En ironment and carbon use efficiency. Plant, Cell and EnŠironment 21: 315–342. 21: 573–588. Paembonan SA, Hagihara A, Hozumi K. 1992. Long-term respiration in Eamus D, Pritchard H. 1998. A cost-benefit analysis of leaves of four relation to growth and maintenance processes of the aboveground Australian savanna species. Tree Physiology 18: 537–545. parts of a hinoki forest tree. Tree Physiology 10: 101–110. Farquhar GD, von Caemmerer S, Berry JA. 1980. A biochemical model Penning de Vries FWT. 1975. The cost of maintenance processes in of photosynthetic CO# assimilation in leaves of C$ species. Planta plant cells. Annals of Botany 39: 77–92. 149 : 78–90. Penning de Vries FWT, Brunsting AHM, van Laar HH. 1974. Products, Farrar JF. 1995. The respiratory source of CO . Plant, Cell and # requirements and efficiency of biosynthesis: a quantitative ap- EnŠironment 8: 427–438. proach. Journal of Theoretical Biology 45: 339–377. Geiger DR. 1975. Phloem loading. In: Zimmerman MH, Milburn JA, Penning de Vries FWT, van Laar HH, Chardon MCM. 1983. eds. Transport in plants. I Phloem loading. Encyclopedia of plant Bioenergetics of growth of seeds, fruits and storage organs. In: physiology. New Series Vol 1. Berlin: Springer-Verlag, 395–431. Proceedings of the symposium on potential productiŠity of field crops Gifford RM. 1994. The global carbon cycle: a viewpoint on the missing Š sink. Australian Journal of Plant Physiology 21: 1–15. in different en ironments, 1980. Manila, Philippines: International Gifford RM. 1995. Whole plant respiration and photosynthesis of Rice Research Institute, 37–59. wheat under increased CO concentration and temperature: long- Phillips DA. 1980. Efficiency of symbiotic nitrogen fixation in legumes. # Š term vs short-term distinctions for modelling. Global Change Annual Re iew of Plant Physiology 31: 29–49. Biology 1: 385–396. Poorter H, Villar R. 1997. The fate of acquired carbon in plants: Goetz SJ, Prince SD. 1998. Variability in carbon exchange and light chemical composition and construction costs. In: Bazzaz FA, utilization among boreal forest stands: implications for remote Grace J. eds. Plant resource allocation. London and New York: sensing of net primary production. Canadian Journal of Forest Academic Press, 39–72. Research 28: 375–389. Pregitzer KS, Laskowski MJ, Burton AJ, Lessard V, Zak DR. 1998. Heldt H-W. 1997. Plant biochemistry and molecular biology. Oxford: Variation in sugar maple root respiration with root diameter and Oxford University Press. soil depth. Tree Physiology 18: 665–670. Ho LC. 1988. Metabolism and compartmentation of imported sugars Raven JA. 1976. The quantitative role of ‘dark’ respiratory processes in sink organs in relation to sink strength. Annual ReŠiew of Plant in heterotrophic and photolithotrophic plant growth. Annals of Physiology 39: 355–378. Botany 40: 587–602. Cannell and Thornley—Modelling the Components of Plant Respiration 53

Reich PB, Oleskyn J, Tjoelker MG. 1996. Needle respiration and Sprugel DG. 1990. Components of woody-tissue respiration in young nitrogen concentration in Scots Pine populations from a broad Abies amabilis (Dougl.) Forbes trees. Trees 4: 88–98. latitudinal range: a common garden test with field-grown trees. Thornley JHM. 1970. Respiration, growth and maintenance in plants. Functional Ecology 10: 768–776. Nature 227: 304–305. Reich PB, Walters MB, Tjoelker MG, Vanderklein D, Buschena C. Thornley JHM. 1977. Growth, maintenance and respiration: a re- 1998a. Photosynthesis and respiration rates depend on leaf and interpretation. Annals of Botany 41: 1191–1203. root morphology and nitrogen concentration in nine boreal tree Thornley JHM. 1982. Interpretation of respiration coefficients. Annals species differing in relative growth rate. Functional Ecology 12: of Botany 49: 257–263. 395–405. Thornley JHM. 1997. Modelling allocation with transport\conversion Reich PB, Walters MB, Ellsworth DS, Vose JM, Volin JC, Gresham C, processes. SilŠa Fennica 31: 341–355. Bowman WD. 1998b. Relationships of leaf dark respiration to leaf Thornley JHM. 1998. Grassland dynamics. Wallingford: CAB nitrogen, specific leaf area and leaf life-span: a test across biomes International, UK. and functional groups. Oecologia 114: 471–482. Thornley JHM, Cannell MGR. 1996. Temperature forest responses to Ryan MG. 1991. Effects of climate change on plant respiration. carbon dioxide temperature and nitrogen: a model analysis. Plant Š Ecological Applications 1: 157–167. Cell and En ironment 19: 1331–1348. Ryan MG. 1995. Foliar maintenance respiration of subalpine and Thornley JHM, Johnson RL. 1990. Plant and crop modelling. A boreal trees and shrubs in relation to nitrogen content. Plant, Cell mathematical approach to plant and crop physiology. Oxford: and EnŠironment 18: 765–772. Oxford Science Publications. Ryan MG, Lavigne MB, Gower ST. 1997. Annual carbon cost of Thornley JHM, Cannell MGR. 2000. Modelling the components of Annals of Botany 85 autotrophic respiration in boreal forest ecosystems in relation to respiration: representation and realism. : 55–67. species and climate. Journal of Geophysical Research 102: Van der Werf A, Kooiman A, Welschen R, Lambers H. 1988. Respiratory 28871–28883. energy costs for the maintenance of biomass for growth and for Ryan MG, Hubbard RM, Pongracic S, Raison RJ, McMurtrie RE. ion uptake in roots of Carex diandra and Carex acutiformis. 1996a. Foliage, fine-root, woody-tissue and stand respiration in Physiologia Plantarum 72: 438–491. Pinus radiata in relation to nitrogen status. Tree Physiology 16: Van der Werf A, Van den Berg G, Ravenstein HJL, Lambers H, Eising 333–343. / R. 1992. Protein turnover: a significant component of maintenance Ryan MG, Hunt ER, McMurtrie RE, Agren GA, Aber JD, Friend AD, respiration in roots? In: Lambers H, Van der Plas LHW, eds. Rastetter EB, Pulliam WM, Raison RJ, Linder S. 1996b. Molecular, biochemical and physiological aspects of plant res- Comparing models of ecosystem function for temperate description / piration. The Hague: Academic Publishing, 483–492. and validation. In: Breymeyer AI, Hall DO, Melillo JM, Agren Veen BW. 1980. Energy cost of ion transport. In: Rains DW, Valentine GI, eds. Global change: effects on coniferous forests and grasslands. RC, Hollaender A, eds. Genetic engineering of osmoregulation. SCOPE. Chichester: John Wiley and Sons, 313–362. New York: Plenum Press, 187–195. Ryle GJA, Powell CE, Gordon AJ. 1979. The respiratory costs of Vierstra RD. 1993. Protein degradation in plants. Annual ReŠiew of nitrogen fixation in soybean, cowpea and white clover. Journal of Plant Physiology and Plant Molecular Biology 44: 358–410. Experimental Botany 30: 135–144. Waring RH, Landsberg JJ, Williams M. 1998. Net production of Simpson FB. 1987. Hydrogen reactions of nitrogenase. Physiologia forests: a constant fraction of gross primary production. Tree Plantarum 69: 187–190. Physiology 18: 129–134. Scheurwater I, Cornelissen C, Dictus F, Welschen R, Lambers H. 1998. Yamaguchi J. 1978. Respiration and the growth efficiency in relation to Why do fast- and slow-growing grass species differ so little in their crop productivity. Journal of the Faculty of Agriculture (Hokkaido rate of respiration, considering the large differences in rate of UniŠersity) 59: 59–129. growth and ion uptake? Plant, Cell and EnŠironment 21: 995–1005. Ziska LH, Bunce JA. 1998. The influence of increasing growth Sheehy JE. 1987. Photosynthesis and nitrogen fixation in legume temperature and CO# concentration on the ratio of respiration to plants. CRC Critical ReŠiews in Plant Sciences. Boca Raton, photosynthesis in soybean seedlings. Global Change Biology 4: Florida: CRC Press Inc, 121–159. 637–643.

APPENDIX In the second step, bound hydrogen, 2 [H], represented by 1 molecule of NADH, is oxidized to water by the respiratory The yield of energy (ATP) and\or reducing power (NADH) chain in mitochondria. This generates energy, and can be from glucose oxidation is by no means a solved problem. written: We give a simplified account; further details can be found j j j 4 j j e.g. in Heldt (1997, chapter 5). 2 [H] O r ADP r Pi H#O H#O r ATP. The oxidation can be regarded as comprising two parts. r \ \ First, glucose is degraded to CO and bound hydrogen, [H]: The ratio is known as the P O or the ADP O ratio. It is # sometimes asserted that this crucial ratio, r l 3, although 4 j j realistically, its value is not precisely known, and it could be glucose 6CO# 2 ATP 24 [H]. a variable depending on metabolic conditions. For example, This reaction is the net result of the oxidation of glucose to measurements on isolated mitochondria have given lower pyruvate by the glycolytic pathway: values, of r l 2n5. ATP formation occurs via the ‘chemi- osmotic’ mechanism which involves proton gradients across 4 j j glucose 2 pyruvate 2 ATP 4 [H], membranes, so there are possibilities for ion leakage and other effects changing the yield of ATP. and the oxidation of pyruvate by the citric acid cycle: Further difficulties are that glucose oxidation to CO# and 4 j bound [H] may proceed along other pathways, e.g. the 2 pyruvate 6CO# 20 [H]. ‘pentose oxidative pathway’, with different stoichiometry We have assumed all these 20 bound [H] are the same, which and products, and that the oxidation of bound hydrogen is is not the case (16 are NADH-[H], 4 are FADH#-[H]). possible without yielding ATP at all, using alternative 54 Cannell and Thornley—Modelling the Components of Plant Respiration dehydrogenases or oxidases which are not coupled to oxidation of 1 molecule of glucose equal to 30 ATP. Hence, proton transport and ATP generation. for a process whose molecular requirement for energy and In our calculations of respiratory costs we assume that all reducing power alone is for a ATPjn NADH, this is bound [H] are equivalent, with 1 molecule glucose equivalent considered as a glucose requirement of (a\30jn\12) glucose to 24 [H] or 12 NADH, and with the ATP yield from the molecules.