Journal of Experimental Botany, Vol. 55, No. 400,
Understanding Photosynthetic Performance Special Issue, pp. 1167±1175, May 2004
DOI: 10.1093/jxb/erh141 Advance Access publication 7 May, 2004
The slow reversibility of photosystem II thermal energy
dissipation on transfer from high to low light may cause
large losses in carbon gain by crop canopies: a
theoretical analysis
Xin-Guang Zhu1, Donald R. Ort1,2, John Whitmarsh2,* and Stephen P. Long1,²
1
Departments of Plant Biology and Crop Sciences, University of Illinois, 190 Plant and Animal Biotechnology
Laboratories, 1201 W Gregory Drive, University of Illinois, Urbana, IL 61801-3838, USA
2
USDA-ARS, University of Illinois, 190 Earl R. Madigan Laboratories, 1201 W Gregory Drive,
University of Illinois, Urbana, IL 61801-3838, USA
Received 2 December 2003; Accepted 2 March 2004
Abstract
Regulated thermal dissipation of absorbed light
energy within the photosystem II antenna system
helps protect photosystem II from damage in excess
light. This reversible photoprotective process
decreases the maximum quantum yield of photosystem II (Fv/Fm) and CO2 assimilation (FCO2), and
decreases the convexity of the non-rectangular hyperbola describing the response of leaf CO2 assimilation
to photon ¯ux (q). At high light, a decrease in FCO2
has minimal impact on carbon gain, while high thermal energy dissipation protects PSII against oxidative
damage. Light in leaf canopies in the ®eld is continually ¯uctuating and a ®nite period of time is required
for recovery of FCO2 and q when light drops below
excess levels. Low FCO2 and q can limit the rate of
photosynthetic carbon assimilation on transfer to low
light, an effect prolonged by low temperature. What is
the cost of this delayed reversal of thermal energy dissipation and FCO2 recovery to potential CO2 uptake by
a canopy in the ®eld? To address this question a
reverse ray-tracing algorithm for predicting the light
dynamics of 120 randomly selected individual points
in a model canopy was used to describe the discontinuity and heterogeneity of light ¯ux within the canopy. Because photoprotection is at the level of the
cell, not the leaf, light was simulated for small points
of 104 mm rather than as an average for a leaf. The predicted light dynamics were combined with empirical
equations simulating the dynamics of the lightdependent decrease and recovery of FCO2 and q and
their effects on the integrated daily canopy carbon
uptake (A¢c). The simulation was for a model canopy of
leaf area index 3 with random inclination and orientation of foliage, on a clear sky day (latitude 44° N, 120th
day of the year). The delay in recovery of photoprotection was predicted to decrease A¢c by 17% at 30 °C and
32% at 10 °C for a chilling-susceptible species, and by
12.8% at 30 °C and 24% at 10 °C for a chilling-tolerant
species. These predictions suggest that the selection,
or engineering, of genotypes capable of more rapid
recovery from the photoprotected state would substantially increase carbon uptake by crop canopies in
the ®eld.
Key words: Leaf canopies, photoprotection, photosynthesis,
reverse ray-tracing, yield loss.
Introduction
Light is the source of energy for photosynthesis, but on
most days plants encounter light ¯uxes that exceed their
photosynthetic capacity. As light levels increase, a process
that operates within the antenna ensemble of photosystem
* Present address: Center for Bioinformatics and Computational Biology, NIGMS/National Institute of Health, 45 Center Drive, Bethesda, MD 20892-6200,
USA.
²
To whom correspondence should be addressed at the Department of Plant Biology. Fax: +1 217 244 7563. E-mail: [email protected]
Journal of Experimental Botany, Vol. 55, No. 400, ã Society for Experimental Biology 2004; all rights reserved
1168 Zhu et al.
II (PSII) is progressively engaged which harmlessly
discharges a portion of photon ¯ux energy as heat.
Thermal dissipation of absorbed light helps protect the
photosynthetic apparatus from damage, particularly by
controlling the rate of damage to the D1 protein of PSII
(Long et al., 1994). Although photodamage has been
documented in crops grown outside their ancestral geographic range, the vast majority of plants in native habitats,
and most crops under cultivation, deal successfully with
excess light avoiding photodamage even under daunting
environmental challenges (Ort, 2001). The process of
photoprotection has been extensively reviewed (Aro,
1999; Long et al., 1994; Ort, 2001). Despite the intensity
of study at the molecular to leaf level, remarkably little is
known about the quantitative impact of photoprotection on
carbon gain at the whole plant level and at the canopy level;
i.e. is it relevant to crop production in the ®eld?
The increased thermal dissipation due to photoprotection lowers the maximum quantum yield of PSII (maximum FPSII³, indicated by Fv/Fm), which in turn results in a
lower maximum quantum yield of CO2 assimilation
(FCO2), i.e. a reduced initial slope in the response of
photosynthetic CO2 assimilation rate (A) to photosynthetic
photon ¯ux density (Q) (Long et al., 1994). This competition for excitation energy between thermal dissipation
and photochemistry not only decreases FCO2, but also the
convexity (q) of the non-rectangular hyperbolic response
of A to Q (Leverenz et al., 1990). q re¯ects the transition
from the initial slope of the light response curve (FCO2) and
asymptote where the maximum assimilation rate (Asat) is
achieved. A q near 1 represents an abrupt transition in
the in¯uence of FCO2 and Asat on A with respect to Q,
while low q (approaching 0) represents a long transition
in which both FCO2 and Asat determine A across the full
range of Q (Leverenz et al., 1990). The decrease in q
coupled with a decrease in FCO2 that occurs during a
photoprotective response is signi®cant because it
increases the light level at which A will be depressed by
any decrease in FCO2 (Long et al., 1994). At lightsaturation, when photoprotection of PSII is most likely to
be fully engaged, the resulting decrease in FCO2 will by
de®nition have no effect on CO2 assimilation. When light
levels decline, FCO2 and q recover, but recovery is not
instantaneous. When a leaf is transferred to lower light,
FCO2 and q will determine photosynthetic rate, and A will
remain below the potential value for that light level until
the readjustment of the photoprotective state appropriate
for that light level is complete. How much loss of carbon
gain does this lag in recovery cause in a canopy in the
®eld?
Photon ¯ux within a canopy of leaves in the ®eld is
highly discontinuous and heterogeneous in space and time
³
All terms are de®ned in Appendix 1.
(Pearcy, 1990; Pearcy et al., 1994). Photon ¯ux at any
point within a canopy will ¯uctuate during the course of
the day, not only because of intermittent cloud cover, but
also because of transient shading by the overlap of leaves
of different canopy layers. As solar angle changes,
individual mesophyll cells of the leaf may pass from full
sunlight to shade within a second. In this varying light
environment, photoprotection, expressed as decreased
Fv/Fm and FCO2, may be predicted from light history and
È gren and SjoÈstroÈm,
temperature (Long et al., 1994; O
1990). Canopy microclimate models have been developed
to predict the diurnal course of the average Q at different
levels within canopies (dePury and Farquhar, 1997;
Forseth and Norman, 1993), which have, in turn, been
used to predict the effect of photoprotection on daily total
È gren and
carbon assimilation (Long et al., 1994; O
SjoÈstroÈm, 1990; Werner et al., 2001). These studies
concluded that the effect of photoprotection on daily
total carbon assimilation is small, but nevertheless signi®cant. However, these studies did not consider the spatial
heterogeneity of Q within leaf layers of canopies.
Averaging removes the abrupt transitions in light that
will occur at the level of the photosynthetic cells and may
underestimate losses. These earlier studies are extended
here by capturing and quantifying this spatial variability
due to the changing solar angle over the course of the day.
This was achieved by determining the diurnal Q at a large
number of randomly selected individual points within a
model canopy. In turn, the light dynamics were used to
estimate decrease and recovery of FCO2 and q at each
point, and then daily carbon assimilation. By summing the
effects at a large number of randomly selected points, the
effect of the slow dynamics of photoprotection readjustment/recovery on daily carbon assimilation by a whole
canopy was estimated. This simulation takes full account
of the dynamic and highly heterogeneous Q within a
canopy due to solar angle and the dynamic nature of the
photoprotective state as indicated by decline and recovery
of FCO2 and q. These simulations demonstrate that the lag
in recovery from the photoprotective state can have a very
substantial effect on daily canopy carbon assimilation,
compared with the hypothetical situation of instantaneous
recovery.
Materials and methods
Any prediction of potential carbon loss in a canopy due to
photoprotection requires three sub-models: (1) a phenomenological
model of photoprotection in response to light history to predict how
de®ned change in light affects FCO2 and q at different temperatures;
(2) a reverse ray tracing algorithm to predict the dynamics of photon
¯ux at any speci®c point within a three-dimensional canopy of
leaves; and (3) a dynamic model of the effect of photoprotection on
canopy carbon assimilation linking (1) and (2) to predict canopy
photosynthesis.
Regulated thermal dissipation of absorbed light
Phenomenological model of photoprotection
Empirical studies have shown that the response of CO2 uptake (A) to
Q can be described effectively for higher plants by a non-rectangular
hyperbola (equation 1) (Long et al., 1994). The parameters of this
relationship are FCO2, q, and Asat; where Asat was assumed to be a
constant as 25 mmol m±2 s±1 in this study, which is an approximate
average for healthy C3 leaves (Long, 1985). Diurnal ¯uctuation in
photoprotection represents a dynamic balance between decrease and
recovery of FCO2 and q. For a given point on a leaf, change in FPSII
over the day is calculated from a cumulative weighted light dosage
(Iint) over the past 24 h (equation 2.1). Equation 2.1 weights light
such that the effect of a high light event diminishes with the time
which has elapsed since that event (Long et al., 1994). Equation 2
determines Fv/Fm from Iint using the empirically derived constant fh
and Tf. Given the same Iint, the decrease of Fv/Fm is less as
temperature (T) increases. This is simulated using an empirical
factor Tf (equation 2.2; Fig. 2) based on data on maize (Aguilera
È gren and SjoÈstroÈm, 1990). The value of fh
et al., 1999) and willow (O
for cold-tolerant species was parameterized based on a photoinhibiÈ gren and SjoÈstroÈm, 1990). To do this,
tion experiment on willow (O
the diurnal clear-sky Q for the 199th and the 200th day of the year in
UmeaÊ, Sweden was predicted based on the Sun±Earth geometry and
atmospheric transmittance after Campbell (1977); the diurnal Iint for
the 200th day of the year was simulated following equation 2.1. The
value of fh was then estimated based on the maximal Iint in the 200th
day, the reported maximal percentage decrease of Fv/Fm (20%), and
the air temperature at the time of the maximum decrease of Fv/Fm
È gren and SjoÈstroÈm, 1990). The fh for cold-susceptible species was
(O
determined similarly based on the percentage decrease of Fv/Fm and
the applied light and temperature conditions in a photoinhibition
experiment on maize (Aguilera et al., 1999). Figure 3 shows an
example of predicted Fv/Fm for a cold-tolerant species given a
dynamic diurnal light ¯uxes.
Fv/Fm is the maximum quantum yield of PSII photochemistry for
quanta absorbed by the pigments associated with PSII complexes.
Variation in the maximum quantum yield of CO2 ®xation for
quanta absorbed by leaves showed a strong linear and positive
relationship with variation in Fv/Fm (BjoÈrkman and Demmig, 1987;
Genty et al., 1989; Long et al., 1994). Such an empirical relationship
between Fv/Fm and FCO2 (equation 3) (Demmig and BjoÈrkman,
1987) was used in this study to predict FCO2 from simulated Fv/Fm.
The coupled decrease in q and FCO2 is simulated using equation 4,
where fc is the ratio of the decrease of q to the decrease of FCO2 with
È gren and SjoÈstroÈm
Iint; fc is assumed to be 1 in this study after O
(1990).
qA2 ± (FCO2Q + Asat)A ± FCO2QAsat = 0
Iinf Tf
…Fv =Fm † ˆ 0:815 1 ÿ
fh
Iint ˆ
iˆ
1440
X
iˆ1
ÿ
Qi
1 ÿ iÿ1
60
(1)
…2†
1169
Fig. 1. Principle of reverse ray tracing. A virtual canopy of 1 m in
height was divided into 12 layers, with a leaf area index of 0.25 in
each layer. Circular leaves of 1 cm diameter were randomly
distributed in each layer. To determine photosynthetic photon ¯ux
density of point P in a given layer n, one reverse ray was issued from
P upward to layer (n±1) along the reverse direction of a direct solar
beam. If the intersection of the reverse ray with any overlying layer
(n±1, n±2, ¼, 1) fell within any leaf, the reverse ray ended and point
P was therefore shaded (Case 1); otherwise, the reverse ray left the
canopy without intercepting any overlying leaves, then the leaf was
sunlit (Case 2).
Fig. 2. The empirical temperature factor relating the relative decrease
of Fv/Fm to temperature at the same Iint. The empirical relationship,
Tf=0.0033T2±0.1795T+3.4257 (R2=0.98), was based on data for willow
È gren and SjoÈstroÈm, 1990) and for maize
as a chilling-tolerant plant (O
as a chilling-intolerant plant (Aguilera et al., 1999).
…2:1†
Tf = 0.0033T2 ± 0.1795T + 3.4257
(2.2)
FCO2 = 0.1367(Fv/Fm) ± 0.0106
Fmax ÿ FCO2
q ˆ qmax 1 ÿ fc
Fmax
(3)
…4†
Reverse ray-tracing algorithm
A model crop canopy of 1 m height was divided into 12 layers of
equal depth (8.3 cm). Each layer was assumed to have the same leaf
area index of 0.25 (Fig. 1). The top layer was assigned as the ®rst
layer and the bottom as the 12th layer. All leaves were assumed to be
circular (1 cm diameter) and randomly distributed in each layer, with
the limitation that, within a layer, one leaf could not overlap another.
Ten points on leaves were chosen by random coordinates within
each layer. A reverse ray-tracing algorithm was used to calculate Q
for each point over 24 h at 1 s intervals; described as follows.
6:28…D ‡ 10†
d ˆ ÿ23:5 cos
…5†
365
ft = 0.262(t ± to)
(6)
Al = arcsin(sind cosl + cosl cosd cosft)
(7)
1170 Zhu et al.
number of sunlit points to the total number of all points. Idiff and Itrans
were assumed to be uniform within a given leaf layer (equations
13.1, 13.2).
Q(p,n) = Idirect + Itrans(n) + Idiff(n)
(13)
where
Itrans(n) = Idirect 3 p(n±1) 3 LAI(n±1) 3 0.1 + (Itrans(n±1) +
Idiff(n±1)) 3 LAI(n±1) 3 0.1
(13.1)
Idiff(n) = (1 ± LAI(n±1)) 3 (Idiff(n±1) + Itrans(n±1))
QA = Q(p,n) 3 0.9
Fig. 3. Predicted diurnal photosynthetic photon ¯ux
maximum quantum yield of PSII (represented by
photoprotection coef®cient, de®ned as the decrease
proportion to Fmax, at a random point in the third
hypothetical canopy described in Fig. 1.
density (Q),
Fv/Fm) and
of FPSII in
layer of the
cos d sin l cos ft ÿ cos l cos d
Az ˆ arccos
cos Al
…8†
Zi = arccos(sin d sin l + cos d cos l cos ft)
(9)
1
Xn ˆ Xnÿ1 ÿ tgZi cos Az
12
…a; t < t0 †
…10†
1
tgZi cos Az
12
…b; t > t0 †
…10†
Xn ˆ Xnÿ1 ‡
Yn ˆ Ynÿ1 ÿ
1
tgZi sin Az
12
…11†
1
12
…12†
Zn ˆ Znÿ1 ‡
To determine photosynthetic photon ¯ux density (Q) of incident
light on one of the selected points (P) in a given layer (n), one reverse
ray is issued from P towards the overlying layer (n±1) along the
reverse direction of the solar beam, which is determined by Sun±
Earth geometry for a speci®c time and latitude (Campbell, 1977)
(equations 5±9, 16). The intersection of the reverse ray with the
plane of layer (n±1) is predicted based on the coordinates of P, the
direction of the reverse ray and the plane of layer (n±1) (equations
10±12). If the intersection fell within any leaf in layer (n±1), the
reverse ray ends and P is assumed to be in shade at that time;
otherwise, the reverse ray continues travelling upwards to the next
layer (n±2) and so on until the intersection falls within a leaf in one
of the upper layers (case 1) or the reverse ray leaves the canopy
without intercepting any leaf (case 2) (Fig. 1). In case 1, P receives
diffuse light (Idiff(n)) and transmitted light (Itrans(n)). In case 2, point P
receives direct sunlight (Idirect) together with Idiff(n) and Itrans(n)
(equation 13), i.e. point P is in a sun¯eck. It was assumed that leaves
absorb 90% of the total intercepted light energy and the remaining
10% was transmitted, emerging in the form of diffuse light from the
leaf lower surface to the immediate lower layer (equation 14). This
absorbance is an average for healthy leaves as measured with an
integrating sphere (Long and HaÈllgren, 1993). The proportion of leaf
area receiving direct sunlight (p(n)) is determined by the ratio of the
(13.2)
(14)
Idirect and diffuse sunlight above the canopy (Idiff(1)) were determined
(equations 15±19) from Sun±Earth geometry and atmospheric
transmittance after Campbell (1977).
Idirect = Ip 3 sin q
(15)
sin q = sin l sin d + cos l cos d cos 15(t ± t0)
(16)
Ip = am Ip0
(17)
mˆ
Pr
Pro sin j
Idiff…1† ˆ 0:51p0 …1 ÿ am † sin j
…18†
…19†
Dynamic model of effects of photoprotection on canopy
carbon assimilation
The total daily canopy photosynthetic carbon assimilation (A¢c) was
calculated by integrating A over the day at each randomly sampled
point in the canopy and then summing the average for each of the 12
layers (equation 20). The diurnal Idiff(1) and Idirect incident above the
canopy was simulated for the 120th day of the year, at latitude 44° N.
To calculate A¢c, the reverse ray-tracing algorithm (equations 5±19)
was ®rst used to predict diurnal Q for 10 randomly chosen points at
each of 12 canopy layers. Iint for a point at any given time was then
calculated based on Q of the past 24 h for that point (equation 2.1).
FCO2 and q were determined from Iint and T (equations 2±4).
Photosynthetic rate (A) at each point was then determined by
substituting values of I, FCO2, and q, as calculated above, into
equation 1.
Ac represents total daily photosynthetic carbon assimilation of the
whole canopy assuming no decrease in Fv/Fm, and correspondingly
FCO2 and q, i.e., assuming FCO2 = Fmax and q=qmax throughout the
day. The loss of total carbon assimilation due to photoprotection was
calculated as decrease in A¢c relative to Ac (equation 21).
A0c ˆ
120
…
… 1440
A…Q…t† ; q…t† ; FCO2…t† †
…20†
iˆ1 tˆ0
Pd ˆ
Ac ÿ A0c
Ac
…21†
Results
Great spatial and temporal heterogeneity in Q were
predicted within the hypothetical model canopy (Fig. 4).
Points on leaves in the upper layers of the canopy received
Regulated thermal dissipation of absorbed light
1171
Fig. 5. Percentage of light incident in the form of direct light as a
proportion of total (Qdirect /Qtotal) at different layers in the canopy on
the 120th Julian day, 44° N latitude. Each point represents the average
value 61 SE of the Q at ten randomly chosen points.
Fig. 4. Examples of predicted diurnal Q of one random point in each
of six different layers within the hypothetical model canopy. Photon
¯ux above the canopy is simulated from Sun±Earth geometry on 120th
day of the year at 44° N, assuming a clear sky.
more direct sunlight than lower layers of the canopy and
most sun¯ecks were predicted to occur in clusters (Fig. 4).
The proportion of daily total light incident as direct light
(Qdirect/Qtotal) progressively decreases with depth into the
canopy (Fig. 5). At layer 1, Qdirect /Qtotal is 0.87; at layer 3,
it is about 0.8 and at layer 10, just 0.1 (Fig. 5).
At 20 °C simulated Fv/Fm of the uppermost canopy layer
of a chilling-tolerant species over the diurnal period varied
from 0.815 at 06.00 h to 0.63 at 14.00 h, but from 0.815 to
0.5 for a chilling-susceptible species over the same time
interval (Fig. 6). The decrease in Fv/Fm was progressively
less with depth into the canopy for both chilling-tolerant
and chilling-susceptible species (Fig. 6A, B).
Great variation in photosynthetic rates was predicted as
a result of the temporal and spatial variation in Q at
different layers of the canopy (Fig. 7). The decrease in
daily total canopy carbon assimilation (A¢c) due to
photoprotection was much greater in the upper layers.
For example, decreased daily total photosynthetic canopy
carbon assimilation in the top four layers of the simulated
chilling-tolerant canopy was 11±24% compared with
negligible decreases below layer 8 (Fig. 8).
For a chilling-tolerant species, the decrease of A¢c due to
photoprotection (i.e. by comparison to Ac) was c. 12.8%,
14.6%, and 24% at 30 °C, 20 °C, and 10 °C, respectively
(Fig. 9). For the hypothetical chilling-susceptible species,
decrease in A¢c was c. 17.3%, 19.7%, and 32% at 30 °C,
20 °C, and 10 °C, respectively (Fig. 9; Table 1). These
results suggest that if full account is taken of spatial
Fig. 6. Predicted diurnal maximal quantum yield of PSII (represented
by Fv/Fm) of one randomly chosen point in ®ve different layers of the
canopy. The light dynamics were as Fig. 4. Temperature was kept
constant at 20 °C. (A) Chilling-tolerant species; (B) chillingsusceptible species.
heterogeneity, loss of photosynthetic ef®ciency due to
photoprotection could cost a canopy 12±30% of A¢c over a
diurnal cycle simply due to loss of ef®ciency and delay in
recovery when diurnal changes in light and dynamic
shading cause sudden decreases in photon ¯ux (Fig. 9).
Discussion
The simulation shows that decreased maximum ef®ciency
of photosynthesis in high light results in a loss of potential
carbon gain when change in solar angle places a point
on one leaf in the shade of another leaf. This loss
continues until thermal dissipation is readjusted to the
1172 Zhu et al.
Fig. 9. Percentage decrease of the daily integral of total canopy
photosynthetic carbon assimilation A¢c due to photoprotection for
chilling-tolerant and chilling-susceptible species at different
temperatures. The values of Q and temperature were as in Fig. 6.
Table 1. Predicted photosynthetic CO2 uptake of different
layers.
Fig. 7. Predicted diurnal photosynthetic rates in different layers of the
canopy. The simulation was for a chilling tolerant species. The values
of Q and temperature were as in Fig. 6.
Simulations were done for a chilling-susceptible species on 120th
Julian day, 44° N latitude assuming constant canopy temperature of
20 °C. Ac is the canopy carbon gain assuming no photoprotective
reduction in q and FCO2; A¢c is the canopy carbon gain with
photoprotective reduction in q and FCO2.
LAI 0±0.5
LAI 0.5±1
LAI 1±1.5
LAI 1.5±2
LAI 2±2.5
LAI 2.5±3
Total canopy
Percentage decrease
Fig. 8. Predicted percentage decrease of the total daily integral of
photosynthetic carbon assimilation in different canopy layers. The
values of Q were as in Fig. 6. (A) Chilling-tolerant species; (B)
chilling-susceptible species.
level appropriate for a lower light level. Accumulated
across a canopy such losses amount to between 12.8% and
30% of total potential carbon gain. The simulation
suggests that considerable gain in carbon assimilation in
Ac
(mol m±2 d±1)
A¢c
(mol m±2 d±1)
2.25
1.49
0.87
0.46
0.24
0.13
5.45
±
1.57
1.21
0.78
0.44
0.24
0.13
4.38
19.7
crop canopies in the ®eld could be achieved if these
decreases in ef®ciency could be avoided by more rapid or
instantaneous readjustments to thermal dissipation. As
noted in the Introduction, these decreases in ef®ciency
ful®l a necessary function of decreasing the probability of
oxidative damage to the D1 protein, which would lower
photosynthetic ef®ciency, termed photodamage, and
require repair and replacement of the protein before
ef®ciency could be restored. In the longer term a continued
excess of excitation energy would lead to irreversible
photo-oxidation (reviewed by Long et al., 1994). Could the
loss found here be decreased without the risk of photodamage and photo-oxidation? Falkowski and Dubindky
(1981) identi®ed algae associated with corals that could
withstand 1.53 full sunlight without evidence of loss of
maximum photosynthetic ef®ciency or photoinhibition,
showing that the loss of ef®ciency is not an intrinsic
requirement of the photosynthetic apparatus, although this
tolerance to high light could reside in an enhanced ability
to repair and replace photodamaged protein D1 rapidly. In
Regulated thermal dissipation of absorbed light
higher plants, Wang et al. (2002) have shown a close
correlation between increased rate of recovery from the
photoprotected state and increased biomass production in
the `super-high yield' rice cultivars.
This theoretical analysis uses a hypothetical canopy
with uniform leaf size and division area between layers.
The direction of the solar beam and canopy structure
parameters, i.e. leaf orientation, leaf inclination, and leaf
area index, are primary determinants of sun¯eck patterns
(Barradas et al., 1998, 1999; Denicola et al., 1992).
Canopies with different structural parameters show
different sun¯eck patterns (Barradas et al., 1998, 1999;
Chazdon, 1988; Pearcy, 1990; Pearcy et al., 1990). Is
discontinuity in light levels with time in the hypothetical
canopy realistic? The predicted diurnal light dynamics
simulated here with a reverse ray-tracing algorithm
showed two major characteristics: (1) sun¯ecks are
clustered in time (Fig. 4); (2) Qdirect/Qtotal was greater in
the upper layers of the canopy than in the lower layers
(Fig. 5). These predictions are qualitatively consistent with
®eld measurements (Pearcy et al., 1990).
Although the operating quantum ef®ciency of PSII (F¢m)
is different and might not necessarily re¯ect changes in
Fv/Fm, this study used the predicted Fv/Fm to infer FCO2,
based on the linear relationship between Fv/Fm and FCO2
as suggested previously (BjoÈrkman and Demmig, 1987;
Genty et al., 1989; Long et al., 1994). In the model, FCO2
will only determine A directly at very low light, when
F¢v /F¢m approaches or equals Fv/Fm. Several different
empirical models have been developed to simulate the
decrease of Fv/Fm for a given light history using different
formulae to calculate a weighted light dose (Iint) (Long
È gren and SjoÈstroÈm, 1990; Valladares and
et al., 1994; O
Pearcy, 1999; Werner et al., 2001). These different
formulae were developed for different crop or tree species
and for different environmental conditions. In the current
study, the empirical model of Long et al. (1994) describing
the decrease of Fv/Fm due to photoprotection was used,
except that the light history used was extended to the past
24 h. The reasoning was that recovery of FCO2from the
photoprotective state may take 2±3 d in cool conditions
(Farage and Long, 1986).
Werner et al. (2001) found, through simulation, a daily
carbon loss of 7.5±8.5% of potential carbon gain in upper
sunlit canopy layers and a 3% decrease in lower layers
of the canopy, and an overall loss of 6.1% for a
Mediterranean evergreen oak Quercus coccifera under
climate conditions which cause mild photoprotection.
Long et al. (1994) estimated a daily total carbon loss of
9% through simulation for a similar climate and a generic
C3 canopy. However, these studies did not predict the rapid
decrease in light that occurs at individual points within the
canopy. When the transient photosynthetic rates under
dynamic light conditions are considered, this simulation
showed that photoprotection caused a loss in daily total
1173
photosynthetic carbon uptake of 12.8±24% due to delayed
recovery for a chilling-tolerant species on the 120th day of
the year at 44° N (Fig. 9). The latitude used in the
simulation was 44° N and was chosen as intersecting many
of the major agricultural production areas of the northern
hemisphere. Temperature and LAI also approximate to
mean conditions that are likely in early summer. In this
study, light conditions were predicted for a clear sky.
Temporal ¯uctuations in Q due to intermittent cloud cover
were not incorporated, but would almost certainly increase
the losses predicted here, by further increasing the
frequency of abrupt transitions in Q.
There is inter- and intra-speci®c variation in rates of
decrease and recovery of Fv/Fm during and following
exposure to excess light (Long et al., 1994). The combination of chilling temperature and high light often leads to a
more severe and prolonged photoprotective response
(Long et al., 1994). The impact of photoprotection on
carbon gain in plants with different chilling tolerance was
simulated using different fh values. As expected, photoprotection was predicted to cause much greater carbon loss
for cold-susceptible species compared with cold-tolerant
species (Fig. 9). Furthermore, photoprotection was predicted to cause much greater carbon loss at low temperature, especially for chilling-susceptible species. For a
chilling-susceptible species on the 120th day of the year at
44° N, photoprotection would decrease daily total photosynthetic carbon assimilation by 17.3% at 30 °C, but 32%
at 10 °C. Lower temperatures cause a greater decrease of
Fv/Fm (Fig. 2) and by assumption, lower FCO2 and q
(equations 2, 4) explaining the simulated larger carbon
loss.
In conclusion, simulating the spatial and temporal
heterogeneity of light in canopies and incorporating the
cost of delayed recovery in photosynthetic ef®ciency on
transfer from high to low light may provide a more
accurate prediction of the loss of diurnal carbon gain due to
photoprotection. The decrease in diurnal total carbon
uptake is between 12.8±32% depending on light conditions, temperature, and chilling tolerance of plant species.
These are almost certainly conservative estimates as these
analyses only considered the spatial heterogeneity of Q
within leaf layers of canopies caused by changes in solar
angle. Nastic and tropic movements of leaves, movement
caused by air currents, and intermittent cloud will cause
dynamic heterogeneities perhaps as signi®cant as those
due to changing solar angle. These results suggest that the
selection or engineering of genotypes better able to recover
more rapidly from the photoprotective state, more tolerant
to photodamage, and thereby able to function with smaller
photoprotective decreases in Fv/Fm, could substantially
increase carbon uptake by crop canopies. The occurrence
of organisms, which can resist any signi®cant reduction in
Fv/Fm in high light, suggest that such changes are possible.
1174 Zhu et al.
Acknowledgements
This work was supported by a grant to SPL and JW from the
National Center for Supercomputing Applications (NCSA) and by a
fellowship from the Physiological and Plant Molecular Biology
training program of the University of Illinois to X-GZ.
Appendix I. List of variables, constants, parameters
Abbreviation
Full name
Unit
A
a
Ac
A¢c
Asat
Az
Rate of photosynthetic leaf CO2 uptake
Atmospheric transmittance
Daily total photosynthetic canopy CO2 uptake without photoprotection
Daily total photosynthetic canopy CO2 uptake with photoprotection
A at saturating light, a constant in this study assumed as 25
Azimuth angle, angle of the deviation from north of the line connecting the point of observation and the point
that sun projects on earth vertically (northern hemisphere)
Day of year
Ratio of relative change of q to relative change of FCO2
Empirical constant in determining the decrease of Fv/Fm for a given Iint. For cold-susceptible species, fh is
5.13105; for cold-tolerant species, fh is 73105
Hour angle, the angular distance from local median, Greenwich UK
Maximum quantum yield pf PSII
The average photosynthetic photon ¯ux density in the form of diffuse light at layer n
Photosynthetic photon ¯ux density of direct sunlight
Weighted light dose at point P at time t
Direct solar radiation on a surface perpendicular to the beam
Solar constant at the top of the atmosphere
Photosynthetic photon ¯ux density of transmitted light at layer n from leaves of the immediate upper layer
Leaf area index
Optical airmass number
Layer number, n=1, 2, ¼12
Randomly selected point on a leaf in a certain canopy layer
Photosynthetic photon ¯ux density
Photosynthetic photon ¯ux density absorbed by leaf
Photosynthetic photon ¯ux density at point P at layer n
Photosynthetic photon ¯ux density at ith min counting backward from the current time for which Iint is
calculated
The daily total photosynthetic photon ¯ux as direct light in a given layer
The daily total photosynthetic photon ¯ux in a given layer
Air pressure at a given location (105)
Air pressure at sea level (105)
Proportionate decrease of canopy assimilation due to photoprotection
Probability that a leaf is in direct sunlight at layer n
Time in hours (0~24)
Temperature
Empirical factor relating the relative decrease of Fv/Fm to temperature
Time of solar noon (12.00 h)
X coordinate of intersection point of reverse ray with upper layer
Y coordinate of intersection point of reverse ray with upper layer
Z coordinate of intersection point of reverse ray with upper layer
Zenith angle
Solar declination angle, the angle between light ray and the equatorial plane of the earth
Solar elevation angle
Initial and maximum slope of non-rectangular hyperbolic response of A to Q
Quantum yield of PSII
The convexity of non-rectangular hyperbolic response of A to Q
Maximum q (0.95)
Maximum FCO2(0.1)
Latitude (44° N)
mmol m±2 s±1
Dimensionless
mol m±2 d±1
mol m±2 d±1
mmol m±2 s±1
Radians
D
fc
fh
ft
F¢v/F¢m
Idiff(n)
Idirect
Iint
Ip
Ipo
Itrans(n)
LAI
m
n
P
Q
QA
Q(p,n)
Qi
Qdirect
Qtotal
Pr
Pro
Pd
p(n)
t
T
Tf
to
X(n)
Y(n)
Z(n)
Zi
d
j
FCO2
FPSII
q
qmax
Fmax
l
Note: Values in parenthesis represent values used in this study.
d
Dimensionless
Dimensionless
Radians
Dimensionless
mmol m±2 s±1
mmol m±2 s±1
Dimensionless
mmol m±2 s±1
mmol m±2 s±1
mmol m±2 s±1
Dimensionless
Dimensionless
Dimensionless
Dimensionless
mmol m±2 s±1
mmol m±2 s±1
mmol m±2 s±1
mmol m±2 d±1
mmol m±2 d±1
Pa
Pa
Dimensionless
Dimensionless
h
°C
Dimensionless
h
Dimensionless
Dimensionless
Dimensionless
Radians
Radians
Radians
Dimensionless
Dimensionless
Dimensionless
Dimensionless
Dimensionless
°
Regulated thermal dissipation of absorbed light
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