Annals of Botany 81 : 421–430, 1998
Dynamic Model of Leaf Photosynthesis with Acclimation to Light and Nitrogen
J. H. M. T H O R N L E Y
Institute of Terrestrial Ecology (Edinburgh), Bush Estate, Penicuik, Midlothian EH26 0QB, UK
Received : 26 August 1997
Accepted : 19 November 1997
A simple model of photosynthesis in a mature C leaf is described, based on a non-rectangular hyperbola : the model
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allows the high-light asymptote of that equation (Pmax) to respond dynamically to light and nitrogen. This causes the
leaf light response equation to acclimate continuously to the current conditions of light and N nutrition, which can
vary greatly within a crop canopy, and through a growing season, with important consequences for gross production.
Predictions are presented for the dynamics of acclimation, acclimated and non-acclimated photosynthetic rates are
compared, and the dependence of leaf properties on light and N availability is explored. There is good correspondence
of predictions with experimental results at the leaf level. The model also provides a mechanism for a down regulation
of photosynthesis in response to increased carbon dioxide concentrations, whose magnitude will depend on
conditions, particularly of nitrogen nutrition.
# 1998 Annals of Botany Company
Key words : Leaf, photosynthesis, hyperbola, model, C , acclimation, light, nitrogen.
$
I N T R O D U C T I ON
Photosynthesis is the initial process driving the growth of
crops and of plant ecosystems. It is affected by the past
environment as well as the current environment and thus its
prediction is a dynamic problem. Thus, we are used to
thinking in terms of an immediate response (within minutes)
of photosynthetic rate to current conditions of light, carbon
dioxide and temperature, summarized by a response
function with certain parameters. Acclimation is a slower
process (taking several days) by which the plant adjusts the
parameters of the photosynthetic response function by
making changes to metabolic pools and possibly morphology. The acclimated photosynthetic response function
has parameters whose values depend on an average of
environmental conditions over the past week or two.
Acclimation of photosynthesis to light (Prioul, Brangeon
and Reyss, 1980 ; see Robson, Ryle and Woledge, 1988, for
a review) and to nitrogen (N) supply can be substantial
(Hirose and Werger, 1987 b ; Evans and Terashima, 1988 ;
Evans, 1989 ; Hollinger, 1996). Furthermore, the effects of
irradiance and N nutrition on photosynthetic capacity are
related (Hirose and Werger, 1987 b ; Evans and Terashima,
1988 ; Zhang and Allen, 1996 ; Murthy, Zarnoch and
Dougherty, 1997). Light and N supply vary greatly over a
growing season in temperate climates. Acclimation of
photosynthetic characteristics to these seasonal changes is
seldom taken into account when calculating photosynthesis.
Also, within a canopy of moderate to high leaf area index
(LAI), there may be a wide range of light environments and
foliage N contents (Hikosaka and Terashima, 1996). It is
therefore desirable that leaf photosynthesis models should
represent acclimation to light and nitrogen supply, so that
both within-canopy and seasonal effects can be considered.
The objective of the present study is to describe a model
where acclimation to light and to N availability of leaf N
0305-7364}98}030421­10 $25.00}0
content and photosynthetic response arise from a single
mechanism, embedded in a leaf-level phenomenology which
is easily tested and parameterized at the leaf level and is
moreover suitable for calculations of canopy photosynthesis
in crop and plant ecosystem models.
Many models of leaf photosynthesis are static. That is,
given values of say irradiance, ambient CO concentration
#
and temperature, the model predicts photosynthetic rate,
but not its time course. It is assumed that a steady state is
achieved instantaneously. Any temporal variations in
irradiance, ambient CO concentration and temperature are
#
followed immediately, without a time lag. Any pools
appearing in such static models are assumed to be small, so
that, given a change in conditions, the pool concentration
moves very rapidly to its new steady-state value. This
approach, which leads to a diminishing-returns photosynthetic response, was pioneered by Maskell (1928) who
constructed an ordinary rectangular hyperbola response
equation, developed further by Rabinowitch (1951) who
introduced CO diffusion resistance and obtained a non#
rectangular hyperbolic equation, and also by Chartier
(1966). The method has since been pursued by many
authors with numerous variations.
The non-rectangular hyperbola (NRH) gives an excellent
phenomenological description of leaf photosynthesis (e.g.
Hirose and Werger, 1987 b), and as such, we use it as the
basis of our acclimation model. We could have used, equally
easily, the simpler rectangular hyperbola (RH), and followed
an exactly analogous method. We chose to use the NRH
rather than the RH because empirically it is far superior and
theoretically it has some modest advantages.
Arguably, a view which is gaining ground is that the
NRH is a suitable equation for use in higher-level models of
crops and plant ecosystems, whereas the problems of
understanding the parameters of the NRH in terms of
underlying biochemistry and molecular biology, can be
bo970575
# 1998 Annals of Botany Company
422
Thornley—Leaf Photosynthesis with Acclimation to Light and Nitrogen
regarded as a separate, although important, project. This
position agrees with views expressed by de Wit (1970) : that
it is important not to try to encompass too many levels of
description when modelling complex systems, and that
sharply focused modules should be used within large models
where possible. A module such as is provided by the NRH
can integrate and support two research communities by
serving as a common component : (1) for those working
towards an understanding of crop and plant ecosystems,
these modules constitute the bottom level of their system ;
and (2) for those working on improving our understanding
of say leaf photosynthesis, the module with its wellcharacterized phenomenology and parameterization can
constitute the top level of their own researches (Thornley,
1980).
Pleaf ¯
THE MODEL
Symbols, definitions, parameter values and units are listed
in the Appendix. The abbreviations DM ¯ dry mass and
XDM ¯ structural dry mass are used in equations.
Leaf photosynthesis
Leaf gross photosynthetic rate, Pleaf (kg CO m−# s−"),
#
depends on the light incident on the upper leaf surface, Ileaf
(J PAR m−# s−"), according to a non-rectangular hyperbola
(NRH)
0 ¯ ξP#leaf®Pleaf(αΙleaf­Pmax)­αIleaf Pmax.
ξ ¯ 0±5,
(1)
α ¯ 1¬10−) kg CO (J PAR)−" [¯ 0±0494 mol CO
#
#
(mol PAR)−"].
This equation has three parameters : ξ, α and Pmax. It is
illustrated in Fig. 1 for four values of ξ. ξ determines the
sharpness of the knee of the curve. Although there is some
evidence that ξ varies with growth light environment and
ξ = 0.999
Leaf photosynthesis,
Pleaf (10–6 kg CO2 m–2 s–1)
0.7
ξ = 0.95
0.6
Pmax
Asymptote
ξ = 0.5
0.5
0.4
ξ = 0 (rectangular hyperbola, RH)
0.3
0.2
0.1
α
0.0
0
Initial slope = photosynthetic efficiency
50
250
100
150
200
Light incident on leaf, Ileaf (J PAR m–2 s–1)
F. 1. Non-rectangular hyperbola for leaf photosynthesis. Equation
(1) is plotted for α ¯ 1¬10−) kg CO J−" [0±0494 µmol CO (mol
#
#
PAR)−"], Pmax ¯ 0±667¬10−' kg CO m−# s−" (15 µmol CO m−# s−").
#
#
Four different values of the ‘ sharpness ’ parameter ξ are shown,
with ξ ¯ 0 corresponding to the rectangular hyperbola.
10−' kg CO ¯ 23 µmol CO . 1 J PAR ¯ 4±6 µmol PAR.
#
#
with tissue N content (Hirose and Werger, 1987 b), it is
assumed constant in our analysis. α [kg CO (J PAR)−"] is
#
the initial slope of the light response curve, and is often
called the photosynthetic efficiency. The value used in eqn
(1) and Fig. 1 is rounded, but is typical of C leaves (e.g.
$
Hirose and Werger, 1987 b). α does not depend on growth
irradiance or N content to a significant degree (Prioul et al.,
1980 ; Hirose and Werger, 1987 b ; Gastal and Be! langer,
1993). Pmax is the instantaneous high-light asymptote of eqn
(1) : Ileaf U ¢, Pleaf U Pmax. Pmax is determined by the concentration of photosynthetic N according to eqn (10). This
allows acclimation to light and N supply to occur.
The NRH of eqn (1) and Fig. 1 is quadratic in Pleaf, with
the solution
αIleaf­Pmax®o[(αIleaf­Pmax)#®4ξαIleaf Pmax]
. (2)
2ξ
The properties of the NRH have been discussed by many
authors (e.g. Thornley and Johnson, 1990). The rectangular
hyperbola (RH) is a special case of the NRH (Fig. 1). The
RH is still preferred to the NRH by some workers on the
grounds of simplicity. The acclimation model presented
below works equally well with either the RH or the NRH.
I have chosen to use the NRH because it is empirically
superior to the RH : it is able to fit a much wider range of
leaf photosynthetic response data. The RH can be obtained
from the NRH by putting ξ ¯ 0 in eqn (2) ; this involves
taking the limit as ξ U 0 and is rather tedious. It is easier to
put ξ ¯ 0 in eqn (1) which immediately gives the RH :
Pleaf ¯ αIleaf Pmax}(αIleaf­Pmax).
Leaf Šariables
The scheme assumed for the acclimation model is given in
Fig. 2, for a single mature leaf connected to a root.
Processes such as the utilization of C and N substrates for
growth, and the utilization of C substrate for maintenance,
are omitted. It is formulated so that the extension of the
approach to a multi-leaf plant or canopy is straightforward.
There are three state variables : the masses of C substrate, N
substrate, and photosynthetic N, in the leaf (Appendix).
These three state-variable pools represent aggregated biochemical species whose definition is inevitably imprecise. It
is envisaged that C substrates consist of water soluble
carbohydrates and any other fairly easily metabolizable
carbohydrates ; N substrates are mostly amino acids and
other mobile forms of N ; photosynthetic N is largely
rubisco. The three state variables are dynamic quantities
whose temporal behaviour gives rise to photosynthetic
acclimation. However, the acclimation model as presented
here for a non-growing leaf in a non-growing plant is
independent of C substrate dynamics, although this would
not be the case when these simplifying assumptions are
relaxed.
A constant leaf area of Aleaf ¯ 0±001 m# (10 cm¬1 cm) is
assumed. Leaf mass comprises the three metabolic statevariable pools just introduced, plus a ‘ structural ’ mass
component, envisaged as being principally cellulose. In a
Thornley—Leaf Photosynthesis with Acclimation to Light and Nitrogen
423
Photosynthesis, Pleaf (2)
Leaf C substrate (15):
mass, MCS,leaf
concn, CS,leafX
Leaf N substrate (18):
mass, MNS,leaf
concn, NS,leafX
rC,leaf
(14)
rN,leaf
Lightdriven (11)
Leaf photosynthetic
N (13):
mass, MNph,leaf
concn, Nph,leafX
Degradation (12)
(16)
rC,root
Root C
substrate:
mass, MCS,root
concn, CS,rootX
rN,root
Root N
substrate:
mass, MNS,root
concn, NS,rootX
F. 2. Model of leaf acclimation to light and N supply. The r­subscript variables denote transport-resistance parameters [eqn (8)]. Growth and
maintenance processes are omitted from this simple model. Leaf photosynthetic N determines the photosynthetic parameter Pmax through eqn (10)
(Fig. 1), giving photosynthetic acclimation to light and N supply. The model has three state variables, shown in the upper three boxes. The
numbers in parentheses refer to equations for fluxes, or when within boxes, to differential equations.
leaf or plant growth model, structural mass may be
synthesized, but is not metabolized. With a structural
specific leaf area of SLA ¯ 25 m# [kg structural dry mass]−",
the structural dry mass (XDM) of the leaf, MX,leaf, is
A
MX,leaf ¯ leaf ¯ 0±04¬10−$ kg XDM.
SLA
(3)
The concentrations of substrate C, substrate N and
photosynthetic N, per unit of structural dry mass, are
M
M
M
CS,leafX ¯ CS,leaf , NS,leafX ¯ NS,leaf , Nph,leafX ¯ Nph,leaf .
MX,leaf
MX,leaf
MX,leaf
(4)
With a constant concentration of structural N of
NX,leaf ¯ 0±008 kg structural N (kg structural dry mass−"),
the total leaf nitrogen content (kg N) is
MN,leaf ¯ MX,leaf(NX,leafX­NS,leafX­Nph,leafX).
(5)
Thus, while the structural N concentration of the leaf is
constant, the substrate N and photosynthetic N concentrations are variables [eqn (4)]. The value of 0±8 % for NX,leaf
provides a floor for the leaf N content, and is chosen to be
compatible with observed values, and also to be satisfactory
in the present context. A wide range of total leaf N
concentrations has been observed, ranging from 0±7 to 5 %
(e.g. Fig. 1.2 of Field and Mooney, 1986). Total N content
per unit leaf area is
Nleaf,A ¯
MN,leaf NX,leafX­NS,leafX­Nph,leafX
¯
.
Aleaf
SLA
(6)
Equations (5) and (3) have been substituted to give the
second expression. An N concentration of 1 % of structural
dry mass corresponds to a superficial N concentration of
0±4¬10−$ kg N m−#.
Root parameters
Root structural dry mass (XDM), substrate C and
substrate N concentrations are assumed to be constant at
MX,root ¯ MX,leaf,
CS,rootX ¯ 0±02 kg C substrate (kg XDM)−",
(7)
NS,rootX ¯ 0±011 kg N substrate (kg XDM)−".
The structural dry mass root : shoot ratio is constant and
equal to unity. In a plant growth model all these quantities
would vary.
Transport resistances
Resistances to substrate C and N transport are associated
with the leaf and root separately (Fig. 2), and summed to
give overall resistances between leaf and root, with
(Thornley, 1997)
rC,leaf ¯
rN,leaf ¯
ρC
ρC
,r
¯
,r
¯ rC,leaf­rC,root ;
MX,leaf C,root MX,root C,leaf–root
ρN
ρN
,r
¯
,r
¯ rN,root­rN,leaf ;
MX,leaf N,root MX,root N,root–leaf
(8)
ρC ¯ 0±2 d, ρN ¯ 2 d.
All resistances have units of d (kg structural dry mass)−". ρC
and ρN are resistivity parameters.
424
Thornley—Leaf Photosynthesis with Acclimation to Light and Nitrogen
Pmax of the photosynthesis light response
Photosynthetic N per unit leaf area is (kg photosynthetic
N m−#)
M
(9)
Nph,leafA ¯ Nph,leaf .
Aleaf
It is assumed that Pmax of eqn (1) is proportional to Nph,leafA,
with
Pmax ¯ cPmax,N Nph,leafA,
(10)
cPmax,N ¯ 0±001 kg CO s−" (kg photosynthetic N)−".
#
The standard value of photosynthetic N content is
0±00042 kg photosynthetic N m−# [eqns (9), (13), above eqn
(3)] giving rise to Pmax ¯ 0±42¬10−' kg CO m−# s−"
#
(¯ 9±5 µmol CO m−# s−").
#
Photosynthetic N pool, MNph,leaf
The input to this pool (Fig. 2) is by light-driven synthesis,
and is given by
NS,leafX
Ileaf
INph,leaf ¯ kG,Nph MX,leaf
,
NS,leafX­KNS,leaf Ileaf­KI,leaf
kG,Nph ¯ 0±008 kg photosynthetic N (kg XDM)−" d−",
(11)
KNS,leaf ¯ 0±01 kg substrate N (kg XDM)−",
KI,leaf ¯ 100 J PAR m−# s−".
The units of INph,leaf are kg photosynthetic N d−". MichaelisMenten dependence on N substrate concentration and on
irradiance is assumed. Any C substrate requirement, either
for building blocks or energy, is ignored. Essentially, in
constructing eqn (11) it is assumed that the synthesis of
photosynthetic N (rubisco) is co-limited by the supply of N
substrate (amino acids) and energy (ATP) ; the energy
supply is proportional to light level ; substrate C level is
irrelevant in this approximation. This effect of light in
driving eqn (11) is over and above its effect in driving eqn
(1). Equation (11) is also tentatively supported by many
observations concerning the direct involvement of light
energy in leaf N metabolism (nitrate reductase), and the fact
that there appears to be energy available for this purpose
additional to the requirements of the photosynthetic carbon
reduction cycle for energy (e.g. Lawlor, 1987).
Output from the pool is due to degradation
ONph,leaf ¯ kD,Nph MNph,leaf , kD,Nph ¯ 0±2 d−".
(12)
d−"
corresponds to a half-life of
This decay rate of 0±2
0±69}k ¯ 3±5 d. Peterson, Kleinkopf and Huffaker (1973)
measured turnover rates for rubisco in the range 0±06 to
0±38 d−".
The differential equation for the rate of change of the
photosynthetic N pool is
dMNph,leaf
¯ INph,leaf®ONph,leaf ,
dt
MNph,leaf(t ¯ 0) ¯ 0±42¬10−' kg photosynthetic N.
(13)
The initial concentration of photosynthetic N is Nph,leafX
(t ¯ 0) ¯ 0±0105 kg N (kg structural dry mass)−" [eqns (3)
and (4)].
C substrate pool, MCS,leaf
The only input to this pool is from photosynthesis [eqn
(2), Fig. 2]. Any contribution from the degradation of
photosynthetic N is ignored.
The only output is to the root by transport, with
OCS,leafUroot ¯
CS,leafX®CS,rootX
.
rC,leafUroot
(14)
The transport resistance is calculated in eqn (8).
The differential equation is
dMCS,leaf 12
¯ ¬86400Aleaf Pleaf®OCS,leafUroot,
44
dt
(15)
MCS,leaf(t ¯ 0) ¯ 4±073¬10−' kg substrate C.
The factor of 12}44 is to convert kg CO to kg C. 86400
#
converts per second to per day. The initial concentration of
substrate C is CS,leafX (t ¯ 0) ¯ 0±102 kg substrate C (kg
structural dry mass)−" [eqns (3) and (4)]. This is the steadystate standard value. Note that in the simplified model
presented here, C substrate does not have a functional role.
In the class of plant models where this acclimation submodel
may be used (e.g. Fig. A 1 of Thornley and Cannell, 1997),
C substrate is used for growth, maintenance, is recycled
from senescing plant material, and will interact with N
substrate levels, protein synthesis and Pmax of the photosynthetic response equation (Fig. 1).
N substrate pool, MNS,leaf
N inputs are from the decay of photosynthetic N, with
eqn (12), and from the root by transport [with eqn (8)],
INS,leaf,NphD ¯ ONph,leaf , INS,rootUleaf ¯
NS,rootX®NS,leafX
. (16)
rN,rootUleaf
The sole output is to photosynthetic N synthesis, with eqn
(11)
(17)
ONS,leaf ¯ INph,leaf .
The differential equation for the N substrate pool is
dMNS,leaf
¯ INS,leaf,NphD­INS,rootUleaf®ONS,leaf ,
dt
(18)
MNS,leaf(t ¯ 0) ¯ 0±44¬10−' kg substrate N.
The initial N substrate concentration is NS,leafX
(t ¯ 0) ¯ 0±011 kg substrate N
(kg structural dry mass)−"
[eqns (3) and (4)]. This is the steady-state standard value.
S I M U L A T I O NS
The model was programmed in ACSL (Mitchell and
Gauthier, 1993). Euler’s method of integration was employed (e.g. Thornley and Johnson, 1990) with an integration interval of 0±1 d.
Leaf irradiance doubled
1.2
Pmax
1.0
0.4
0.8
Pleaf
0.6
0.2
0.4
lleaf
0.1
0.0
0
5
10
15
20
25
30
0.2
0.0
Photosynthesis: Pmax, Pleaf
(10–6 kg CO2 m–2 s–1)
Nleaf,A
0.5
0.3
B
0.6
1.4
Leaf N (10–3 kg N m–2)
Irradiance (103 W PAR m–2)
Photosynthesis: Pmax, Pleaf
(10–6 kg CO2 m–2 s–1)
A
0.6
Photosynthetic N
0.012
0.011
Substrate N
0.010
0.009
Structural N
0.008
0
5
10
15
20
25
30
Time, t (days)
Leaf nitrogen [kg N (kg XDM)–1]
Leaf nitrogen [kg N (kg XDM)–1]
0.013
Nleaf,A
0.5
Pmax
0.4
Pleaf
0.3
0.2
NS,rootX
0.1
0.0
C
0.014
Root substrate N doubled
0
5
10
15
20
25
30
1.8
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
Leaf N (10–3 kg N m–2)
Root N substrate [0.1 kg N (kg XDM)–1]
425
Thornley—Leaf Photosynthesis with Acclimation to Light and Nitrogen
D
0.025
Substrate N
0.020
Photosynthetic N
0.015
0.010
Structural N
0.005
0
5
10
15
20
25
30
Time, t (days)
F. 3. Time course of acclimation to light and N. Initially the leaf is in a steady state with leaf irradiance Ileaf ¯ 100 W PAR m−# (460 µmol PAR
m−# s−") and root N substrate concentration NS,rootX ¯ 0±011 kg N substrate (kg structural dry mass)−" [Fig. 2, eqn (7)]. Leaf irradiance is doubled
in A and C on day 10 ; in B and D root N substrate is doubled. Nleaf,A is leaf total N per unit area [eqn (6)] ; Pmax is the asymptote of the leaf light
response [eqns (1) and (10)] ; Pleaf is leaf photosynthetic rate [eqn (2)]. 10−' kg CO ¯ 23 µmol CO . In C and D, leaf photosynthetic N and substrate
#
#
N concentrations are given by eqn (4) ; leaf structural N concentration, NX,leafX [eqn (5), Appendix] is constant. An integration interval of 0±01 d
was used, not for reasons of stability but to obtain better graphs.
Dynamics of photosynthetic acclimation
The model (Fig. 2) provides for acclimation to leaf
irradiance [Ileaf, eqn (1)] and to N supply, represented in the
model by the root N substrate concentration. This is
illustrated in Fig. 3 where the irradiance (Fig. 3 A and C)
and the root N substrate concentration have been doubled
(Fig. 3 B and D).
An increase in irradiance (Fig. 3 A) causes an immediate
shift along the current photosynthesis-light response curve
[eqn (2), Fig. 1] which increases photosynthetic rate Pleaf ,
followed by further gradual change as the asymptote of that
curve (Pmax, Fig. 1) adjusts to the new light level. The time
constant for this latter gradual change depends on the rate
of degradation of photosynthetic N [eqn (12), Fig. 2].
Successive increases in the asymptote Pmax have decreasing
influence on the actual photosynthetic rate Pleaf because at
high Pmax the photosynthetic efficiency α is increasingly
important [with Pmax very large in eqn (1) the solution is
Pleaf ¯ αIleaf]. N content per unit leaf area, Nleaf,A [eqn (6)],
increases in parallel with Pmax [eqn (10)]. The immediate
effect on leaf substrate N (Fig. 3 C) is a decrease, resulting
from leaf substrate N being converted to photosynthetic N
(Fig. 2) faster than it can be replenished from the root N
substrate pool, followed by a return of leaf substrate N to its
former level. Working with grass leaves, Lolium multiflorum,
Prioul et al. (1980) transferred leaves between irradiances of
16 and 110 W PAR m−#, and found that acclimation was
substantially complete after about 6 d, a time scale consistent
with Fig. 3 A.
In Fig. 3 B and D acclimation to increased N availability
is shown. The photosynthetic response is similar to, but
smaller than, the acclimation response to light (Fig. 3 A)
where, as explained above, the latter response is a result of
two mechanisms. There are now two dynamic components
to the increase in total leaf N (Fig. 3 B). First leaf N
substrate increases rapidly in response to the doubling of
root N substrate as N substrate moves in from the root (Fig.
3 D) ; within-plant substrate transport is a relatively rapid
process so this initial transient is substantially complete
within a day. Second there is a slower rise in leaf N due to
increased photosynthetic N synthesis resulting from the
higher leaf N substrate concentration [eqn (11), Fig. 2], and
the photosynthetic N pool moves towards its new equilibrium value (Fig. 3 D) ; the time constant for this second
phase is the same as in Fig. 3 C under doubled leaf
426
A
0.7
0.6
0.5
Pmax, acclimated to 200 W m–2
(asymptote)
0.4
0.3
0.2
Pmax, acclimated to 20 W m–2 (asymptote)
0.1
Pleaf, acclimated to 20 W m–2
0.0
Ratio: Pleaf /Pmax (dimensionless)
Pmax, acclimated
to leaf irradiance
Pleaf, acclimated
to leaf irradiance
Pleaf, acclimated
to 200 W m–2
0
100
200
300
B
1.0
400
2.0
Ratio of Pleaf /Pmax
0.8
Leaf N content:
total
1.5
0.6
1.0
0.4
Photosynthetic
0.5
Substrate
Structural
0.2
0.0
0
100
200
300
–2
Leaf irradiance, Ileaf (W PAR m )
Leaf N (10–3 kg N m–2)
Photosynthesis: Pmax, Pleaf
(10 –6 kg CO2 m–2 s–1)
Thornley—Leaf Photosynthesis with Acclimation to Light and Nitrogen
0.0
400
F. 4. A, Photosynthetic light responses, with and without acclimation.
Solid lines, fully acclimated asymptote Pmax [Fig. 1 and eqn (10)] and
leaf photosynthetic rate Pleaf [eqn (2)] ; dashed lines, leaf photosynthetic
rate Pleaf of leaves acclimated to 20 W m−# (92 µmol m−# s−") and to
200 W m−# (920 µmol m−# s−") ; the asymptotes Pmax are also shown. B,
Ratio of the actual acclimated leaf photosynthetic rate Pleaf at a given
irradiance Ileaf to the Pmax for that irradiance ; the total leaf N content
Nleaf,A and its three components [eqn (6)]. Acclimated values are
obtained by running the dynamic model until a steady state is
achieved (see Fig. 3), typically 100 d. 10−' kg CO ¯ 23 µmol CO .
#
#
1 J PAR ¯ 4±6 µmol PAR.
irradiance and is discussed above. I have not found data on
the dynamics of acclimation of Pmax to N availability. The
model predicts that acclimation to N availability is a little
slower than acclimation to light, due to the root-leaf
resistance causing an extra delay. The dynamics of photosynthetic acclimation in Fig. 3 are such that there will be
only a minor adjustment to diurnal variation in the
environment, but the seasonal changes in environment can
be tracked quite closely, with a time lag of about 5 d. A
more realistic model could include other pathways for N
supply (Dewar, 1993), and other sources of N such as
degradable (non-photosynthetic) structure (Thornley, 1977).
Investigation by Woledge and Pearse (1985) suggest that
leaf age is an important factor in the ability of a leaf to
respond to changes in N availability.
Light-response curŠes for acclimated and non-acclimated
leaŠes
In Fig. 4 A, responses of leaf photosynthetic rate, Pleaf [eqn
(2)], to irradiance, Ileaf, are illustrated. The solid curves are
for a leaf that is fully acclimated at each irradiance level : the
upper solid curve depicts Pmax [Fig. 1, eqns (1) and (10)], the
asymptote of the light response curve, and the lower solid
curve is the actual leaf photosynthetic rate [Pleaf, eqn (2)] at
that irradiance. The ratio of these two quantities is given in
the upper solid curve of Fig. 4 B : although the asymptote
Pmax increases with irradiance, the actual photosynthetic
rate Pleaf approaches the asymptote more closely at higher
irradiances. The instantaneous light response of leaf
photosynthesis [Pleaf , eqn (2)] for high-light (200 W PAR
m−#) acclimated leaves is drawn in the upper dashed curve
and asymptote in Fig. 4 A, and similarly the response for a
low-light acclimated leaf is given in the lower dashed curve
and asymptote. The leaf total N content (Fig. 4 B) responds
positively to irradiance, due to an increasing photosynthetic
N component. In this application, the substrate and
structural components of leaf N are constant, as shown. In
Fig. 4 A, we can compare the photosynthetic rate Pleaf of
leaves fully acclimated to leaf irradiance, with that of leaves
at the same irradiance but which have been acclimated to
200 W m−#. These two curves cross over at about 200 W
m−#. At light levels lower than 200 W m−#, leaves acclimated
to 200 W m−# outperform fully acclimated leaves ; at light
levels higher than 200 W m−#, fully acclimated leaves
outperform leaves acclimated to 200 W m−#.
The results in Fig. 4 compare well with Fig. 1 of Hikosaka
and Terashima (1996), Fig. 2 of Prioul et al. (1980) and Fig.
7 of Hirose and Werger (1987 b).
Effect of N supply on acclimated photosynthetic rate
Nitrogen supply has been varied by assigning different
constant values to the root N substrate concentration (Fig.
2). In a steady-state, non-growing leaf, the N substrate
concentration in root and leaf is equal. This is a
consequence of the model : in the steady state there are no
sinks for N in the leaf ; there is therefore no transport of N
into the leaf and the substrate N concentrations in leaf and
root are equal [eqn (16)]. Leaf N substrate concentration
influences the irradiance-dependent synthesis of leaf photosynthetic N according to eqn (11). Figure 5 illustrates some
properties of the leaf, fully acclimated to light and to N
availability. The responses given were generated by varying
leaf irradiance at each value of the root substrate N
concentration (NS,rootX) given.
Figure 5 A shows linear relationships of light-saturated
photosynthetic rate (Pmax) against total leaf N content
[Nleaf,A, eqn (6)] with the intercept depending on nutrient
supply, in this case the root N substrate concentration,
NS,rootX. The linearity between Pmax and Nleaf,A mostly reflects
the assumed linearity between Pmax and Nph,leafA in eqn (10),
and the assumption of constant leaf structural N in eqn (5).
The intercept varies with the value of NS,rootX because leaf
substrate N concentration equilibrates to a value equal to
the constant root substrate N concentration, NS,rootX ; thus,
steady-state(acclimated)Pmax £ Nph,leafA ¯ Nleaf,A®constant,
and the constant increases with increasing NS,rootX. The
NS,rootX ¯ 0±0055 kg substrate N (kg structural dry mass)−"
line is in excellent agreement with the high-light graph of
Fig. 2 of Hirose and Werger (1987 b) for Solidago altissima,
0.022
0.8
0.7
0.011
0.6
0.5
0.0055
0.4
0.3
0.2
0.1
0.0
C
Leaf N content (10–3 kg N m–2)
NS,rootX values:
1.0
0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2
Leaf N content, Nleaf,A (10–3 kg N m–2)
NS,rootX = 0.0055
Leaf N content: total
0.8
0.6
0.4
Photosynthetic
Structural
0.2
0
Substrate
150
50
100
200
250
Leaf irradiance, Ileaf (W PAR m–2)
B
2.2
2.0
1.8
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
NS,rootX values:
300
427
0.022
0.011
0.0055
0
50
100
200
250
150
Leaf irradiance, Ileaf (W PAR m–2)
300
NS,rootX = 0.022
D
2.5
Leaf N content (10–3 kg N m–2)
Pmax (10–6 kg CO2 m–2 s–1)
A
0.9
Leaf N content, Nleaf,A (10–3 kg N m–2)
Thornley—Leaf Photosynthesis with Acclimation to Light and Nitrogen
Leaf N content: total
2.0
1.5
1.0
Substrate
0.5
Photosynthetic
Structural
100
200
250
50
150
Leaf irradiance, Ileaf (W PAR m–2)
0
300
F. 5. Acclimated leaf properties obtained by running the dynamic model to steady state (see Fig. 3, typically 100 d) with a range of irradiance
levels. Root N substrate concentration NS,rootX has the values shown, with units of kg substrate N (kg structural dry mass)−". A, Relationship
between maximum photosynthetic rate Pmax and leaf N content. B, Leaf N content Šs. leaf irradiance. C and D, The components of leaf N content
Šs. irradiance for the values of N substrate concentration NS,rootX given. The responses in A and B for NS,rootX ¯ 0±011 correspond to the fully
acclimated responses in Fig. 4. 10−' kg CO ¯ 23 µmol CO . 1 J PAR ¯ 4±6 µmol PAR.
#
where the measured CO exchange rate is probably a
#
reasonable approximation to Pmax. There is also satisfactory
qualitative agreement for a montane tropical forest tree,
Tetrorchidium rubriŠenium, as in Fig. 1 of Anten, Hernandez
and Medina (1996).
Figure 5 B illustrates a predicted diminishing-returns
dependence of leaf N content [Nleaf,A, eqn (6)] on leaf
irradiance. This reflects the Michaelis-Menten dependence
of light-driven synthesis on Ileaf [eqn (11)]. This follows
because steady-state photosynthetic N concentration
Nph,leafA is proportional to the input flux INph,leaf [eqns (11) to
(13)], and at the same time the structural concentration of
leaf N, NX,leafX , and the leaf substrate N concentration,
NS,leafX(¯ NS,rootX), are both fixed. Therefore, Nleaf,A ¯
constant¬Ileaf}(Ileaf­KI,leaf)­another constant which depends positively on NS,rootX. A more linear response of Nleaf,A
to Ileaf could be obtained if eqn (11) were more linear in Ileaf .
Figure 5 B is in reasonable agreement with Fig. 7 of Hirose
and Werger (1987 b), who relate the relative radiation range
found within a canopy of S. altissima to leaf N content.
However, Fig. 7 of Hirose and Werger (1987 b) could
arguably support a more linear response of Nleaf,A to Ileaf
#
than is given by our current parameterization. The three
responses in Fig. 5 B are very similar, although, geometrically, the response of leaf N content to irradiance is
largest at the lowest value of root N substrate (0±0055). The
three components of leaf total N are given in Fig. 5 C and D,
illustrating the changing relationships between the substrate,
structural and photosynthetic N pools, and how these
depend on N supply (NS,rootX) and irradiance.
D I S C U S S I O N A N D C O N C L U S I O NS
The non-rectangular hyperbola provides a convenient and
accurate summary of leaf photosynthetic response to
irradiance, and it has been much used for this purpose
(Marshall and Biscoe, 1980 ; Hirose and Werger, 1987 b ;
Pachepsky, Haskett and Acock, 1996). It has also been
widely employed for calculating canopy photosynthesis
(Johnson and Thornley, 1984 ; Jarvis, Miranda and
Muetzelfeldt, 1985 ; McMurtrie, Rook and Kelliher, 1990 ;
Topp and Doyle, 1996).
The most transparent way of calculating instantaneous
canopy photosynthesis from leaf photosynthesis is to sum
428
Thornley—Leaf Photosynthesis with Acclimation to Light and Nitrogen
over the elements of the canopy (but see De Pury and
Farquhar, 1997). This calculational method can be directly
compared with experimental data (e.g. Acock et al., 1978).
However, difficulties of using this approach are : (1)
acclimation of leaf parameters to seasonal changes in N
supply and irradiance (acclimation to temperature is much
weaker, e.g. Robson et al., 1988) ; and (2) acclimation of leaf
parameters to changing position within the canopy, since
position in the canopy affects the local N supply and local
leaf irradiance. The first problem is often ignored by
simulation models. The second problem means that analytical integration through the canopy assuming constant
leaf photosynthesis parameters (e.g. Johnson and Thornley,
1984) may be unacceptably inaccurate. Until recently, the
computational costs of numerically integrating through the
canopy have been substantial, especially for high leaf area
index canopies, and this has given rise to many algebraic
schemes for calculating canopy photosynthesis directly (e.g.
see Sands, 1995, who gives references to earlier work).
However, this is no longer the case, and it seems mistaken
to use complex algebraic schemes with possibly dubious
approximations when direct calculations are feasible.
For instance, it is sometimes assumed that nitrogen is
distributed within the canopy so as to optimize canopy
photosynthesis (e.g. Hirose and Werger, 1987 a). However,
Hollinger (1996) has shown that at least some observed
canopy N allocation patterns do not give maximum canopy
assimilation. Furthermore, in terms of scientific methodology, it is preferable to use a ‘ free ’ or ‘ objective ’ set of
equations and assumptions (Monod, 1974), rather than
what are often highly subjective ‘ optimality ’ or ‘ goalseeking ’ assumptions. Since ‘ goal-seeking ’ controls can
always be represented within an objective framework (e.g.
as factors influencing fluxes), it is methodologically preferable to begin with an objective framework, and to refine
that framework systematically as its failures are identified.
My first aim has been to present a mechanistic approach
to the acclimation problem which modifies the current very
successful leaf-level phenomenology encapsulated in the
non-rectangular hyperbola, and also permits extension to
the evaluation of canopy photosynthesis while avoiding the
use of optimization schemes. A second aim has been to
develop a method which is compatible with the class of crop
growth and plant ecosystem models where (a) plant dry
matter is divided into aggregated biochemical categories
(e.g. ‘ structure ’ and ‘ storage ’ ; Warren Wilson, 1972), and
(b) the process by which dry matter is partitioned between
the different parts of the plant is achieved by the transport
of substrates within the plant, and their utilization (conversion into other components) in those different parts (e.g.
Thornley, 1997). A future investigation will attempt to
combine the acclimation model presented here with the
transport-resistance approach to allocation (Thornley,
1997), in order to examine the distribution of N and
photosynthetic parameters within the crop canopy.
Note that the present model extended to a growing plant
provides a simple mechanism for ‘ down regulation ’ for
leaves exposed to enhanced atmospheric CO concentrations
#
(e.g. Pettersson and McDonald, 1994). Down regulation is
a downward acclimation of Pmax in leaves exposed to
enhanced atmospheric CO concentrations over long
#
periods. The decrease in Pmax is in addition to any decrease
in Pmax produced by decreasing stomatal conductance. The
model of Fig. 2 can predict down regulation of Pmax by the
following route. Increased CO raises sugar levels (C
#
substrates) and decreases N substrate concentrations because growth depends on the product of C and N substrates,
and the sink for N substrates is increased. The synthetic rate
of photosynthetic N is thereby decreased [eqn (11)], and
thus there are decreases in the concentration of photosynthetic N [eqn (13)] and Pmax [eqn (10), Figs 1 and 5 A].
The extent to which this effect occurs will depend on the
conditions, agreeing with the fact that observations of down
regulation have been very variable : Jones, Jongen and
Doyle (1996) and Casella, Soussana and Loiseau (1996)
observed little down regulation, in contrast to the findings
of Korner and Miglietta (1994) and Schappi and Korner
(1996). In a more general context, Cannell and Thornley
(1998) discuss the dependence of CO responses on other
#
factors and in particular N nutrition, which can lead to
apparently inconsistent findings. Their findings will apply
equally to down regulation.
Acclimation to temperature has not explicitly been
considered here. All the fluxes in Fig. 2 depend on rate
parameters which are functions of temperature. In principal,
a different temperature function can apply to each rate
parameter although in practice the temperature functions
for the different rate parameters may be similar. If the
temperature functions are explicitly represented in the
model, then the model could be used to make analogous
predictions to those presented above about the instantaneous and acclimatory responses of the system, including
photosynthesis, to temperature. Plant responses to temperature are highly important, and a significant, perhaps
major, component of the plant’s response to temperature is
due to the instantaneous response to temperature of some of
the parameters of the photosynthetic response function [eqn
(2), Fig. 1]. However, the evidence is that the acclimatory
response to temperature of photosynthesis is small compared
to that to light and nitrogen (e.g. Robson et al., 1988). It has
therefore been ignored in this investigation.
A C K N O W L E D G E M E N TS
I thank Roddy Dewar and an anonymous referee for many
helpful suggestions and comments. The work has been
supported by NERC through its TIGER programme,
Department of the Environment contracts on carbon
sequestration, European Community Epoch and Espace
Projects, and the AFRC Institute of Grassland & Environmental Research (North Wyke).
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430
Thornley—Leaf Photosynthesis with Acclimation to Light and Nitrogen
APPENDIX
Symbols, definitions, units and Šalues
Abbreviations : DM, dry matter ; XDM, structural dry matter ; phN, photosynthetic N ; PAR, photosynthetically active
radiation. Numbers in parentheses refer to the equation where the symbol is introduced. Initial values of the state
variables cause the system to be in a steady state when the ‘ driving ’ variables, leaf irradiance Ileaf and root N substrate
concentration NS,rootX, have their standard values.
State variables
Definition
Initial value
MCS,leaf
MNph,leaf
MNS,leaf
Mass of C substrate in leaf (15)
Mass of photosynthetic N in leaf (13)
Mass of N substrate in leaf (18)
4±0729¬10−' kg substrate C
0±41905¬10−' kg phN
0±44¬10−' kg substrate N
Parameters
Aleaf
CS,rootX
cPmax,N
Ileaf
KI,leaf , KNS,leaf
Definition
Leaf area (3)
C substrate concentration in root (7)
Parameter relating Pmax to leaf N (10)
Leaf irradiance (1) (standard value)
Michaelis-Menten constants in photosynthetic N synthesis (11)
Degradation rate constant of photosynthetic N (12)
Synthesis rate constant for photosynthetic N (11)
Leaf structural dry mass (3)
Root structural dry mass (7)
N substrate concentration in root (7) (standard
value)
N concentration in leaf structure (5)
Resistances to C, N substrate transport associated
with leaf, root (8)
Resistances to C, N substrate transport between leaf
and root (8)
Structural specific leaf area (3)
Photosynthetic efficiency (1)
Sharpness parameter of photosynthetic response (1)
Resistivity parameters for C, N substrates (8)
Values
0±001 m#
0±02 kg substrate C (kg XDM)−"
0±001 kg CO s−" (kg phN)−"
#
100 J PAR m−# s−"
100 J PAR m−# s−", 0±01 kg substrate N
(kg XDM)−"
0±2 d−"
0±008 kg phN (kg XDM)−" d−"
0±04¬10−$ kg XDM
0±04¬10−$ kg XDM
0±011 kg substrate N (kg XDM)−"
Definition
Units
kD,Nph
kG,Nph
MX,leaf
MX,root
NS,rootX
NX,leafX
rC,leaf , rN,leaf ,
rC,root, rN,root
rC,leaf–root,
rN,root–leaf
SLA
α
ξ
ρC, ρN
Other
variables
CS,leafX
INph,leaf
INS,leaf,NphD
INS,rootUleaf
MN,leaf
Nleaf,A
NS,leafX
Nph,leafA
Nph,leafX
OCS,leafUroot
ONph,leaf
ONS,leaf
Pleaf
Pmax
C substrate concentration (4)
Input to photosynthetic N pool (11)
Input to leaf N substrate from photosynthetic N by
degradation (16)
Input to leaf N substrate from root by transport (16)
Total leaf nitrogen (5)
Total N content per unit leaf area (6)
N substrate concentration in leaf(4)
Photosynthetic N per unit leaf area (9)
Photosynthetic N concentration (4)
Output of C substrate from leaf to root (14)
Output from photosynthetic N pool (12)
Output from leaf N substrate pool (17)
Leaf gross photosynthetic rate (2)
Light-saturated photosynthetic rate (1)
0±01 kg structural N (kg XDM)−"
5000 (C), 50 000 (N) d (kg XDM)−"
10 000 (C), 100 000 (N) d (kg XDM)−"
25 m# (kg XDM)−"
1¬10−) kg CO (J PAR)−"
#
0±5
0±2, 2 d
kg substrate C (kg XDM)−"
kg phN d−"
kg substrate N d−"
kg substrate N d−"
kg N
kg N m−#
kg substrate N (kg XDM)−"
kg phN m−#
kg phN (kg XDM)−"
kg substrate C d−"
kg phN d−"
kg substrate N d−"
kg CO m−# s−"
#
kg CO m−# s−"
#