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. C A N N E L L* and J. H. M. T H O R N L E Y
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.
I N T R O D U C T I ON
The need to predict the effect of climate change is promoting
a critical re-examination of ecosystem models, which are
ultimately the only tools we have to forecast the effect of
gradual change over decadal timescales. Empirical or more
mechanistic models of photosynthesis enable gross photosynthesis to be predicted with some confidence (e.g.
Farquhar et al., 1980 ; Cannell and Thornley, 1998). But
having estimated assimilate production quite accurately,
most models then dispense with about half of the assimilate
in respiration and allocate the remainder for the growth
of plant parts using somewhat arbitrary coefficients or
proportions based on widely-ranging observed values (e.g.
A/ gren et al., 1991 ; Ryan et al., 1996 b). In the most
extreme case, respiration is simply subtracted as a fixed
fraction of gross photosynthesis (Coops et al., 1998 ;
Waring et al., 1998).
This, and the following paper (Thornley and Cannell,
2000), re-examines the principles and practice of modelling
plant respiration, with the following two convictions. First,
confidence in predicting future ecosystem responses, as
opposed to describing past data, may be improved by
representing respiration, at least partially, in terms of
* For correspondence. Fax j44(0)1314453943, e-mail mgrc!
ite.ac.uk
0305-7364\00\010045j10 $35.00\0
underlying mechanisms. Respiration is a very large flux ; it
is intimately linked to many other processes—growth,
allocation, nitrogen uptake etc.—and is important in
determining net primary production and plant death. Broadbrush approaches, which ignore mechanisms, may make it
impossible to detect and evaluate a range of possible
responses and may fail to predict important effects.
Second, there have recently been some theoretical and
experimental advances in understanding respiration, e.g. by
Ryan and coworkers (Ryan, 1991, 1995 ; Ryan et al., 1996 a,
1997), Bouma and coworkers (Bouma, 1995 ; Bouma et al.,
1995 ; 1996) and Gifford (1994, 1995). There is now
sufficient new information to justify a re-evaluation of the
old concept of growth and maintenance respiration
(McCree, 1970 ; Thornley, 1970) developed by Thornley
(1977), subsequently extended to include ion uptake by
Johnson (1983, 1990) and still almost universally adopted as
the paradigm for representing respiration in models
(Amthor, 1994, gives an excellent modern statement of this
paradigm).
In this paper, we use the recent literature on plant
respiration to highlight some of the principles that need to
be considered when developing more mechanistic
approaches to plant respiration. We also identify some of
the essential observations that models must be capable
of simulating. This account draws information from
recent reviews of respiration, which offer more comprehensive descriptions of the literature (Lambers et al.,
# 2000 Annals of Botany Company
46
Cannell and Thornley—Modelling the Components of Plant Respiration
1983 ; Amthor, 1984, 1986, 1991, 1994 ; Farrar, 1985 ;
Ryan, 1991 ; Poorter and Villar, 1997 ; Reich et al., 1998 a,
b). The companion paper (Thornley and Cannell, 2000)
then re-examines how respiration is represented in models
and how it may be represented more mechanistically, taking
into account the principles outlined below.
RESPIRATION IS CONTROLLED BY BOTH
ENERGY DEMAND AND THE SUPPLY
O F C S U B S T R A T ES
Mitochondrial respiration consumes C substrates (mostly
glucose) to provide energy (ATP) and reducing power
(NAD(P)H) for all energy-requiring processes in plants.
Figure 1 presents a simplified scheme of the way in which
C substrates are used to generate ATP and NAD(P)H in
support of growth and other processes.
Assuming that the enzymes involved in respiration are
present in excess, rates of respiration may be viewed as
being co-limited by the rate of supply of C substrates (source
or ‘ push ’ limited) and by the demand for ATP and
NAD(P)H by energy-requiring processes, reflected in the
rate of supply of ADP and NAD(P) (sink or ‘ pull ’ limited)
(Farrar, 1985 ; Amthor, 1994). In growing plants, the rates
of most processes requiring ATP or NAD(P)H are themselves dependent on the rate of supply of C substrates either
directly (growth and phloem loading) or indirectly (ion
uptake and protein resynthesis). Consequently, we should
expect the overall demand for ATP and NAD(P)H and
hence the respiration rate to be positively correlated with
the supply rate and\or concentration of C substrates in
the plant (Farrar, 1985, pp. 432–433 ; Amthor, 1994,
pp. 508–509).
A brief discussion of our assumptions regarding glucose
dissimilation, ATP and NADPH production and the P\O
ratio is given in the Appendix.
RESPIRATORY COSTS IN LEAVES MAY BE
LESS THAN EXPECTED FROM THEIR MASS
O R N C O N T E NT
Figure 1 shows that ATP and NAD(P)H can also be drawn
directly from the light reaction of photosynthesis. This
occurs in chloroplasts during the day when there is excess
ATP production and can supply at least part of the energy
required for growth, protein turnover and phloem loading
in leaves without consuming C substrates (Raven, 1976 ;
Lawlor, 1987). In effect, excess energy in the chloroplasts is
used directly to support respiration, avoiding the need to
synthesize sugars and then respire them. Also, during the
night, photosynthetic proteins are not activated, so it is
likely that less ATP is required for protein maintenance.
Thus, the consumption of C substrates for respiration in
leaves may be less than expected from their mass or N
content. Allowance should be made for this in models, e.g.
Photosynthesis
C substrate
(glucose)
C skeletons
(glucose)
for growth
CO2
Respiration
ADP
NAD(P), Pi
(Photosynthesis)
ATP
NAD(P)H
Direct
growth
respiration
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)
Litter
Plant tissue
(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
by adjusting foliage growth and maintenance respiration
coefficients according to current photosynthetic activity.
PROCESSES WITH QUANTIFIABLE
R E S P I R A T O R Y F L U X ES : G R O W TH,
N I T R A T E R E D U C T I ON, N F I X A T I ON,
#
N U P T A K E, O T H E R I O N U P T A K E A N D
PHLOEM LOADING
At least nine plant processes can be separated which require
energy : growth (Penning de Vries et al., 1983 ; Thornley
and Johnson, 1990) ; nitrate reduction, symbiotic dinitrogen
fixation (Simpson, 1987) ; root N-uptake (Bloom et al.,
1992) ; other ion uptake (Thornley and Johnson, 1990, p.
348) ; phloem loading (Geiger, 1975 ; Bouma, 1995), protein
turnover (Vierstra, 1993) ; maintenance of cell ion concentrations and gradients (Bouma, 1995) ; and apparently
wasteful, heat-producing respiration following the alternative (cyanide resistant) pathway or futile cycles (Hue,
1982 ; Lambers, 1985). In this analysis we do not attempt
to separate out respiration associated with secondary metabolism, detoxification of pollutants or all forms of damage
repair.
For each energy-requiring process it is theoretically
possible to define the respiratory cost (in terms of C
substrate consumed, CO emitted or O consumed) per unit
#
#
of process—the specific unit cost. Respiration rate is then
given by :
respiration rate l specific unit costirate of the process
(1)
It is necessary to determine both specific unit cost and the
rate of the process in order to calculate the contribution to
respiration. Specific unit respiratory costs can be approximately quantifiable for six of the nine processes : growth,
nitrate reduction, N fixation, N-uptake, other ion uptake
#
and phloem loading. The rates of five of these six processes
can also be reasonably quantified. For ‘ other ion uptake ’
the flux is quantifiable, but, because of uncertainties
concerning ion leakage and exudation, the gross flux may be
substantially larger than the net flux.
Growth respiration
Growth respiration is defined here in terms of ‘ growth
yield ’, YG, the units of C appearing in new biomass per unit
of glucose C utilized for growth (Thornley, 1970 ; called
‘ growth efficiency ’ by Yamaguchi, 1978, although YG is not
a true efficiency). The ‘ construction cost ’ or ‘ glucose
requirement ’ in units of C of a glucose substrate required
per C unit of new biomass is 1\YG (Penning de Vries et al.,
1983) and the ‘ growth coefficient ’ in units of C respired per
C unit of new biomass synthesized from a glucose substrate
is given by (1kYG)\YG (this is more accurately described as
a ‘ CO production coefficient ’).
#
The parameter YG can be estimated from experimental
data e.g. by using a regression method (see Thornley, 1970)
or calculated theoretically from the chemical composition
of new plant material (Penning de Vries et al., 1974 ;
47
Thornley and Johnson, 1990, p. 352). For most vegetative
plant tissue, the growth yield YG is in the range 0n7 to
0n85 (this is taking account of the direct construction cost
only) equivalent to construction costs or glucose requirements in the range 1n2 to 1n4 g glucose (g dry matter)−"
and CO production coefficients in the range 0n2 to 0n4 g
#
CO (g dry matter)−".
#
For the construction of organic acids with their low
energy content (high oxidation state), YG can range from 1n0
to 2n4 g C in organic acid product per g C in glucose
substrate, with a value of 1n4 for malate. Equivalent values
of YG, in units of g C in product per g C in glucose substrate
are 0n85 to 1n0 for carbohydrates, 0n8 to 0n85 for lignins, 0n7
for lipids (palmitate), and 0n5 to 0n8 for proteins and nucleic
acids, depending on whether the nitrogen source is ammonium or nitrate. Despite this range, the overall construction
cost of vegetative plant biomass is surprisingly constant.
Many experimental estimates of an overall YG give a figure
of about 0n7 g C in product tissue per g C in glucose
substrate, differing by 10 % or less on average between plant
parts, woody and herbaceous species, fast and slow-growing
species and growth conditions, because of covariation
between the classes of constituents in plant biomass (Poorter
and Villar, 1997). However, in plant growth simulators,
where some of the growth costs may be separately accounted
for (e.g. nitrate reduction, phloem loading and N uptake), it
is preferable to use higher values of YG, in the range 0n75 to
0n85, because this now applies more specifically to the direct
biochemical costs of synthesis. Thus, the value(s) for YG
used in models depend on how other components of
respiration are represented.
Nitrate reduction
The full cost of nitrate reduction is 8 mol H (mol N)−"
(e.g. Marschner, 1995, p232), giving rise to a glucose C
requirement for respiration of (8i6i12\24)\14 l 1n72 kg
C (kg nitrate N reduced to ammonia)−", assuming that
glucose with 6 C atoms of relative molecular mass 12 is
equivalent to 24H.
Symbiotic N fixation
#
Symbiotic N fixation requires a minimum of 16 ATP and
#
4 NADPH per mol N fixed (Simpson, 1987 ; Thornley and
#
Johnson, 1990, p. 321) implying a minimum glucose C
requirement for respiration of 2 kg C (kg dinitrogen N
reduced to ammonia)−", although some of the energy in the
hydrogen evolved may be recovered and there are costs in
synthesizing and maintaining a functional rhizobial population. Thus, theoretically, dinitrogen fixation is only slightly
more expensive than the full costs of nitrate reduction, in
the ratio of 2 : 1n72. In practice, however, measured costs of
N fixation are generally higher than minimum values. In
#
units of kg C (kg dinitrogen fixed)−", measured values
averaged 6n5 in the work of Ryle et al. (1979), 5n7 in
the review by Phillips (1980) and 3n1 in the review by Sheehy
(1987, derived from his Fig. 7). Values in the range 4–6 kg
C (kg dinitrogen fixed)−" seem most acceptable.
48
Cannell and Thornley—Modelling the Components of Plant Respiration
N uptake
Bouma et al. (1996) obtained a theoretical specific cost for
nitrate ion uptake of 0n43 mol O (mol NO −)−", assuming the
#
$
ions crossed only one membrane, that 2 mols of H+ were
−
+
required per mol NO , 1 mol H was pumped over a
$
membrane by the hydrolysis of one ATP to ADP and
oxidative phosphorylation (P\O ) had an efficiency of
#
4n7 mol ATP (mol O )−" (0n43 l 2\4n7).
#
+
The cost of ammonium (NH ) ion uptake may be similar
%
to that of potassium (K+), which requires 1 mol H+ per mol
cation (e.g. Marschner, 1995, chapter 2). Thus, NH + may
%
be half as costly to take up as NO −. However, this is an
$
approximation, because there are strong interactions between K+ and NH + uptake. Also, because of pH effects,
%
combinations of NO − and NH + may be especially favoured
%
$
energetically, uptake of NH + alone may cause the plant pH
%
problems, incurring other respiratory costs. Finally, there is
the possibility that NH + may be deprotonated outside the
%
membrane, which it can then enter and cross without
assistance.
Measured uptake is the difference between ion influx and
ion efflux. One explanation for variation in observed costs
of net uptake is variation in efflux, as well as the inclusion
of some costs of maintaining cell ion gradients. Bouma et al.
(1996)’s theoretical estimate of 0n43 mol O (mol NO −)−" is,
#
$
however, consistent with experimental estimates in the
range 0n39–0n67 mol O (mol NO −)−". Previous experimental
#
$
estimates were higher [0n83–1n16 mol O (mol NO −)−" ; Veen,
#
$
1980 ; Van der Werf et al., 1988] as have been more recent
estimates, which suggest that costs are greater for slowgrowing species [Scheurwater et al., 1998 ; 0n41–1n22 mol O
#
(mol NO −)−"].
$
In this study, we assume that the respiratory cost for the
uptake of 14 g NO − N l 1 mol NO − N is 0n5 mol O or
$
#
$
2 mol H+ or 2 mol ATP l 2i6\30 l 2\5 mol C in glucose
respired (assuming 1 mol glucose, C H O , respired yields
' "# '
30 mol ATP) l 12i2\5 g glucose C respired. Therefore, in
mass units, the cost of NO − uptake is (2\5)i(12\14) l
$
0n34 g glucose C respired per g NO − N. For NH + uptake,
%
$
we use 0n17 g glucose C respired per g NH + N taken up. We
%
recognize that the assumption that 0n5 mol O is used in
#
uptake respiration per mol NO − and that the P\O ratio
#
$
is 5 (cf. 4n7 estimated by Bouma et al., 1996), with the
respiration of 1 mol glucose providing 30 ATP (based on
coupled mitochondrial respiration) are all debatable.
derived from gross structural mass times the non-N mineral
concentration (about 4 %, but in reality variable) less an
amount recovered from senescing plant parts.
Phloem loading
The respiratory costs of phloem loading, including all
pathways from starch in the chloroplast to apoplastic
loading of sucrose into the phloem lie, theoretically, in the
range 2n4–4n0 mol ATP (mol sucrose)−", equivalent to
0n5–0n8 mol CO (mol sucrose)−" (assuming 1 CO is
#
#
equivalent to 5 ATP) agreeing well with measured values of
about 0n7 mol CO (mol sucrose)−" (Bouma et al., 1995).
#
This is equivalent to 0n7\12 l 0n06 kg C respired from a
glucose substrate (kg C in sucrose loaded)−". Phloem
unloading is assumed to occur passively through the
symplast and have no respiratory cost (Ho, 1988).
P R O C E S S E S W I T H L E S S -Q U A N T I F I A B L E
R E S P I R A T O R Y F L U X ES : P R O T E I N
T U R N O V E R, C E L L I O N C O N C E N T R A T I O N
M A I N T E N A N C E A N D W A S T A GE
Although there is no clear distinction between quantifiable
and non-quantifiable respiration fluxes, we suggest that, at
present, it is less easy to estimate the specific unit respiratory
costs and\or the rates of the remaining three energyrequiring processes : protein turnover, maintenance of cell
ion concentration and gradients and all forms of wastage
respiration.
Protein turnoŠer
The orderly degradation and resynthesis of proteins is
required for acclimation and development and to enable N
to be used efficiently (Vierstra, 1993). The respiratory costs
can, in theory, be calculated from the specific energy costs
of forming peptide bonds and the degradation constant for
protein turnover (s−"), knowing the amount of N in the
tissue and assuming 1n26 mol N-protein (mol peptide
bond)−" (Bouma et al., 1996). The problem is that both the
energy costs of forming peptide bonds and the degradation
constant can vary by at least a factor of two (De Visser
et al., 1992 ; Van der Werf et al., 1992). Thus, in practice,
there may be no advantage in using eqn (1) to estimate
this component of respiration.
Uptake of other ions
Maintaining cell ion concentrations and gradients
The respiratory cost of the uptake and transport of ions
other than N (P, K, Ca, Mg etc.) has been assumed by
Thornley and Johnson (1990, p. 348) to be 1 H+ or 1 ATP
per ion, equivalent (see above calculation) to (1i6\30 l
1\5)i(12\40) l 0n06 g glucose C respired per g mineral
taken up. This assumes that the mineral relative molecular
mass is 40 and constant—ignoring the fact that, in reality,
the average molecular weight of minerals taken up will
vary.
Whereas for N, the amount taken up can be modelled
explicitly, the uptake of other minerals may simply be
In order to maintain a near-constant environment in the
cytosol, cells need to take up ions to counter ion effluxes or
other losses. The respiratory cost of maintaining cell ion
concentrations and gradients can, in theory, be calculated
from the rate of efflux of ions and a specific cost which
depends on the number of active membrane passages of the
ions and the proton-ion and proton-ATP stoichiometries
(Bouma, 1995, p. 81). However, in practice, there is too little
information on ion gradients in cell and respiratory
pathways to quantify these components in complex multicellular tissues of plants, and, in experimental estimates of
Cannell and Thornley—Modelling the Components of Plant Respiration
respiration, this component is commonly confounded with
the costs of protein turnover in leaves and stems, or with net
ion uptake in roots.
AlternatiŠe pathway respiration and futile cycles
Plant mitochondria possess mechanisms which can oxidize
surplus NADH without generating ATP. This is similar to
wastage respiration produced by futile cycles (Hue, 1982).
Also, the hydrolysis of ATP may not be coupled to energy
requiring processes. The fraction of C substrate that is used
this way is highly variable among tissues, but tends to be
greatest when there are high concentrations of respiratory
substrates, leading to the hypothesis that it represents a
kind of energy overflow (Lambers, 1997). Although unit
respiratory costs could be specified, it is currently impossible
to specify the rate of this component of respiration.
DIFFERENT WAYS OF CLASSIFYING THE
COMPONENT ENERGY REQUIRING
P R O C E S S ES
Growth-maintenance paradigm
The nine processes considered above are normally grouped
together into those associated with ‘ growth ’ and those
associated with ‘ maintenance ’. The growth-maintenance
paradigm may be acceptable and useful for some purposes,
but it should be realized that there is no rigorous division
between growth and maintenance energy-requiring processes (Table 1). Ion uptake and phloem loading have
elements of both growth and maintenance and all forms of
wastage respiration are neither. Also, maintenance is
incomplete in mature plants, because there is some retrieval
of energy and substrates from senescing tissues, possibly
leading to overestimation of maintenance costs. Additionally, growth respiration normally includes the cost of nitrate
reductions, but it could exclude both nitrate reduction and
N uptake respiration if these were accounted for separately
(Johnson, 1990).
Consequently, when using the growth-maintenance
paradigm, the value of YG has to be chosen somewhat
pragmatically, depending on how the other processes are
represented, and the maintenance coefficients must be
regarded as empirical devices with no very rigorous meaning.
Maintenance coefficient values differ between leaves, stems
and roots, because different processes are included, and
some parameter adjustment is normally necessary to give
realistic model performance.
Process-residual approach
An alternative approach is to calculate the respiratory
costs separately for growth in each plant part (perhaps then
better called ‘ local ’ growth respiration), nitrate reduction,
N fixation, N uptake, other ion uptake and phloem
#
loading (the six quantifiable processes) and regard the
remainder as a residual. Residual respiration is then
associated with protein turnover, maintaining cell ion
concentrations\gradients and includes all wastage respiration (and any unidentified components). This residual may
be estimated, like maintenance respiration, by selecting an
appropriate coefficient, which may be termed the ‘ residual
maintenance ’ coefficient and may differ between plant
parts.
The advantages of this approach are that (1) the fraction
of total plant respiration which has to be estimated using an
empirical coefficient is reduced to a minimum, reducing
uncertainty in the overall estimate of respiration, and (2)
information is gained on the energy costs of different
processes, which differ from each other and can vary among
species (Lambers and Poorter, 1992 ; Bryla et al., 1997 ;
Eamus and Prichard, 1998). The disadvantage, of course,
is that many parameters have to be defined for the different processes, some of which are uncertain, as discussed
above.
MAINTENANCE OR ‘RESIDUAL
M A I N T E N A N CE ’ R E S P I R A T I O N M A Y B E A
LESS VARIABLE FUNCTION OF TISSUE
N CONTENT THAN OF BIOMASS
Since a rigorous definition of maintenance respiration is
elusive, it is hardly surprising that it is difficult to measure
a maintenance coefficient unambiguously. Nevertheless,
T     1. Different definitions and classifications of energy-requiring processes in plants
Processes associated Classical growth
with growth (G),
(G) and
maintenance (M)
maintenance
and waste (W)
(M) paradigm
Energy requiring processes
G
Local growth
Nitrate reduction
N fixation
#
N uptake
Other ion uptake
Phloem loading
Protein turnover
Cell ion concs\gradients
Alternative\futile
*
*
*
*
*
*
M
49
W
G
M
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
Processes
represented
(PR) and
residual approach
PR
Residual
*
*
*
*
*
*
*
*
*
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
(1975, table 3), Amthor (1984, table 1) and Amthor (1986,
table A.1) on a mass loss per unit mass per day basis. Values
vary greatly with tissue type, with some typical values being
10−' d−" for seeds, 10−% d−" for stem wood, and up to 0n05 d−"
for leaves and roots. There is also considerable variation
with tissue age and growing conditions.
Many studies, based on the growth-maintenance paradigm, show that maintenance respiration rates of leaves,
stems and roots are more closely related to their Kjeldahl N
contents than to their masses, volumes or surface areas
(Ryan, 1991, 1995 ; Ryan et al., 1996 a ; Pregitzer et al., 1998)
suggesting that maintenance respiration is directly or
indirectly related to tissue protein content (McCree, 1974 ;
Penning de Vries, 1975 ; Thornley, 1982 ; De Visser et al.,
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,
presumably because only part of this lumped respiration
term is directly related to protein content, and, in any case,
the proportionalities between tissue N content, protein
content and respiratory function are variable (see Ryan,
1991 ; Amthor, 1994). For instance, there is a 65 % difference
in the relationship between plant N content and maintenance
respiration reported by Irving and Silsbury (1987) and Ryan
(1991) and a three-fold difference in the rate of leaf dark
respiration per unit N measured by Jones et al. (1978) and
Ryan (1995)" (see also Amthor, 1994 ; Reich et al., 1996,
1998 a, b).
Thus, in practice, coefficients of maintenance respiration
per unit N content have to be chosen with a measured range
based on the emergent behaviour of the model. This
pragmatism applies equally to ‘ residual maintenance ’ as to
maintenance in the growth-maintenance paradigm.
RESPIRATORY FLUXES ASSOCIATED
WITH DIFFERENT PROCESSES VARY
I N D E P E N D E N T LY
As a rule-of-thumb, the ratio of growth to maintenance
respiration in the growth-maintenance paradigm is some-
" Ryan’s (1995, his Fig. 3) value for tree foliage was 2n62 µmol C
respired (mol Kjeldahl N)−" s−" at 10 mC. This converts to a rounded
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−"].
The last item of 0n35 is a consequence of the temperature function
used by Thornley (1988, Fig. 3.6). Ryan’s measurements of gas
exchange were made at night over a 4 h period (2300–0300 h) on fully
expanded foliage. Jones et al. (1978), working with perennial ryegrass,
extended the period of darkness to 46 h, and assumed that the CO
#
efflux between 40 and 46 h represented ‘ maintenance ’ respiration.
They analysed the CO efflux over 48 h of darkness. Protein content
#
was determined by a Kjeldahl determination of N less NO − N mul$
tiplied by 6n25. Their mean value of 85 mg CO (g protein)−" d−" at
#
15 mC converts to a rounded 20 mC value of 0n2 kg C respired
(kg N)−" d−" [multiply by 10−' kg mg−"i12 kg C (44 kg CO )−"
#
i6n25 g protein (g N)−"i1000 gN (kg N)−"i0n7−"].
times taken as approximately unity, averaged over a
season (Sprugel, 1990 ; Amthor, 1994). However, maintenance respiration was estimated to represent 79 % of the
annual above-ground respiration in 13-year-old Chamaecyparis trees in the field in Japan (Paembonan et al.,
1992).
In reality, the activities of meristems and proportions of
meristematic and non-meristematic tissues change during a
season and during the lifetime of plants, especially trees.
Similarly, the rates of individual energy-requiring processes,
such as ion uptake, N fixation and phloem loading, change
#
seasonally and during plant development and also differ
among species and environments. One clear advantage of
the process-residual approach is that these changes and
differences are revealed.
RATIOS BETWEEN RESPIRATION AND
GROSS PHOTOSYNTHESIS ARE
CONSERVATIVE BUT VARIABLE
Because photosynthesis provides the substrate for respiration and associated processes, there is a close coupling
between the amount of C assimilated and that lost by
respiration, so that the ratio of photosynthesis to respiration
is fairly stable when averaged over weeks or longer (CharlesEdwards, 1982, pp. 73–76 ; Dewar, et al., 1998).
There is a substantial literature supporting the classic
observations of McCree and Troughton (1966) that the
carbon use efficiency (CUE : net primary productivity per
unit of C assimilated by photosynthesis) of plants varies
within a restricted range (normally 0n4–0n6) over a wide range
of plant size and environmental conditions. Notable recent
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
#
concentrations ; (2) Monje and Bugbee (1998) over the
vegetative life of wheat ; (3) Ziska and Bunce (1998) on
soybean over a range of temperatures ; (4) Ryan et al.,
(1996 a) on Pinus radiata with extreme irrigation and
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. (1998 a, b) on trees and other
plants, showing close couplings between measured photosynthesis and respiration.
However, it is also clear that CUE is not constant. Models
which assume constancy may overlook important variation
(Coops et al., 1998 ; Waring et al., 1998). Ryan et al.
(1977) found CUE values from 0n36 to 0n68 in Pinus
stands in different environments, and conifers seem to
have substantially smaller CUEs than broadleaved tree
species, perhaps owing to their larger foliage biomass (Goetz
and Prince, 1998). In some circumstances, respiratory costs
can be appreciably less at low temperatures and in high
CO (see Amthor, 1991, 1994). Also, respiration is likely
#
to change as a fraction of C fixation in plants with varying
C storage and may exceed C fixation in plants that are
drying.
Cannell and Thornley—Modelling the Components of Plant Respiration
C O N C L U S I O N S R E G A R D I N G M O D E L L I NG
The principles and facts outlined above provide guidance on
(1) the ways in which respiration may be modelled and (2)
some criteria by which model behaviour might be evaluated.
The main conclusions are summarized below.
Model features
(1) Respiration requires C substrate and is therefore
directly and\or indirectly C substrate dependent,
although it may be stimulated by ADP production
(Amthor, 1994). Thus, in order to be mechanistic and
realistic, models should separate C substrate from
structure so that this dependence can be represented
(remembering that the substrate-structure separation
is itself an approximation). Similar arguments apply
to modelling growth and allocation (Cannell and
Dewar, 1994 ; Thornley, 1997).
(2) Account should be taken of the fact that respiration
in leaves may make a smaller demand on C substrates
than expected from their mass and N content, owing
to the ATP and NAD(P)H supplied by the light
reactions of photosynthesis and the non-activation of
photosynthetic proteins at night. In practice this may
be done using an arbitrary reduction factor, as
mechanistic modelling could require explicit representation of ATP and NAD(P)H pools, photosynthetic dark reactions and time steps of a minute or
less.
(3) It is possible and desirable to distinguish respiration
associated with growth, nitrate reduction, symbiotic
N fixation, N-uptake, other ion uptake and phloem
#
loading, because reasonable estimates can be made of
the specific unit respiratory costs and the rates of
these processes [eqn (1)]. Growth respiration is easily
modelled. A reasonable average direct ‘ growth yield ’
(YG) of plant vegetative tissues is about 0n8 g C
appearing in new biomass per g of C substrate
utilized. Values of the specific unit respiratory costs of
other processes are less certain, but, based on the
earlier discussion, estimates are : for nitrate reduction,
1n7 kg C respired from a glucose substrate (kg nitrate
N)−" but remembering that this value may be greatly
decreased if reduction takes place in the foliage ; for
symbiotic N fixation, 4–6 kg C respired from a
#
glucose substrate (kg dinitrogen N reduced to ammonia)−" ; for N uptake, 0n34 kg C respired from a
glucose substrate (kg nitrate N)−" and half this for
ammonium N uptake ; for the uptake of other ions,
0n06 kg C is respired from a glucose substrate per kg
mineral taken up, and it is assumed that up to 50 % of
the minerals in senescing material can be recycled if it
is required for new growth ; and for phloem loading,
0n06 kg C is respired from a glucose substrate (kg C
loaded)−".
(4) At present, it is less easy to estimate accurately the
specific unit respiratory costs and\or the rates of
protein turnover, maintenance of cell ion concen-
51
trations and gradients and all forms of wastage
respiration.
(5) The growth-maintenance paradigm is valuable, but
there is no rigorous division between growth and
maintenance energy-requiring processes, maintenance
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.
(6) An alternative ‘ process-residual ’ approach is to
estimate explicitly respiratory fluxes associated with
growth, nitrate reduction, symbiotic N fixation, N#
uptake, other ion uptake and phloem loading, and
treat all other respiration (associated with protein
turnover, cell ion concentration and gradient maintenance and wastage) as a residual, represented by an
adjustable phenomenological coefficient. This residual
may be termed ‘ residual maintenance ’ respiration.
(7) There is considerable empirical evidence that maintenance (and presumably ‘ residual maintenance ’)
respiration may be less variable when expressed as a
function of tissue N content rather than of biomass,
volume or surface area.
Model performance
(1) Respiration rates associated with individual processes
are variable individually and in relation to each other
during plant development and seasonally. Clearly, it
can be valuable for models to simulate and predict
this variation in order to gain insight and understanding.
(2) However, ratios between rates of gross photosynthesis
and respiration—and hence the ratio of net to gross
primary production—vary within a limited range
when averaged over weeks or longer, because of the
coupling between respiration and C substrate supply.
This behaviour should be the unforced outcome of
mechanistic models (Thornley and Cannell, 1996 ;
Thornley, 1998) but can, of course, also be used to
model the long-term growth of vegetation in a
descriptive manner without insight or explanation
(Waring et al., 1998).
A C K N O W L E D G E M E N TS
This work has been supported by the European Union EUMEGARICH project. We thank an anonymous referee for
suggesting many improvements to the original manuscript.
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APPENDIX
In the second step, bound hydrogen, 2 [H], represented by
1 molecule of NADH, is oxidized to water by the respiratory
chain in mitochondria. This generates energy, and can be
written :
The yield of energy (ATP) and\or reducing power (NADH)
from glucose oxidation is by no means a solved problem.
We give a simplified account ; further details can be found
e.g. in Heldt (1997, chapter 5).
The oxidation can be regarded as comprising two parts.
First, glucose is degraded to CO and bound hydrogen, [H] :
#
glucose 4 6 CO j2 ATPj24 [H].
#
This reaction is the net result of the oxidation of glucose to
pyruvate by the glycolytic pathway :
glucose 4 2 pyruvatej2 ATPj4 [H],
and the oxidation of pyruvate by the citric acid cycle :
2 pyruvate 4 6 CO j20 [H].
#
We have assumed all these 20 bound [H] are the same, which
is not the case (16 are NADH-[H], 4 are FADH -[H]).
#
2 [H]jOjr ADPjr Pi 4 H OjH Ojr ATP.
#
#
The ratio r is known as the P\O or the ADP\O ratio. It is
sometimes asserted that this crucial ratio, r l 3, although
realistically, its value is not precisely known, and it could be
a variable depending on metabolic conditions. For example,
measurements on isolated mitochondria have given lower
values, of r l 2n5. ATP formation occurs via the ‘ chemiosmotic ’ mechanism which involves proton gradients across
membranes, so there are possibilities for ion leakage and
other effects changing the yield of ATP.
Further difficulties are that glucose oxidation to CO and
#
bound [H] may proceed along other pathways, e.g. the
‘ pentose oxidative pathway ’, with different stoichiometry
and products, and that the oxidation of bound hydrogen is
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
proton transport and ATP generation.
In our calculations of respiratory costs we assume that all
bound [H] are equivalent, with 1 molecule glucose equivalent
to 24 [H] or 12 NADH, and with the ATP yield from the
oxidation of 1 molecule of glucose equal to 30 ATP. Hence,
for a process whose molecular requirement for energy and
reducing power alone is for a ATPjn NADH, this is
considered as a glucose requirement of (a\30jn\12) glucose
molecules.