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Plant Physiol, January 2001, Vol. 125, pp. 42-45
Models of Photosynthesis
Graham D.
Farquhar,*
Susanne
von Caemmerer, and
Joseph A.
Berry
Environmental Biology Group and Cooperative Research Centre
for Greenhouse Accounting, Research School of Biological Sciences,
Australian National University, Australian Capital Territory 0200, Australia (G.D.F.); Molecular Plant Physiology Group, Research School
of Biological Sciences, Australian National University (S.v.C.);
and Department of Plant Biology, Carnegie Institution of Washington,
Stanford, California 94305 (J.A.B.)
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A BRIEF HISTORY |
Our model of photosynthesis (8)
published some 20 years ago in Planta has had an impact and
seen application that far exceeded our expectations. Perhaps it is
useful to reflect on what this model did and why we published it. It is
important to note that our model is not a complete model of
photosynthesis. It makes no attempt to treat all of the steps in this
important process; rather, it was a synthesis, a simplified view of the
already (in 1980) overwhelming knowledge of the contributing mechanisms.
In the years preceding our model a great body of work had accumulated
describing the responses of CO2 exchange by
leaves to a wide range of environmental conditions (temperature,
CO2 concentration, light intensity, humidity, and
oxygen concentration). These responses were quite reproducible, but
difficult to explain. Pieces began to fall into place that informed our
ignorance. Perhaps the pivotal event was the finding by George Bowes
and Bill Ogren that O2 was a competitive
inhibitor of CO2 fixation by Rubisco and an
alternative substrate leading to a side reaction that fueled
photorespiration. Others added findings that integrated
photorespiration into photosynthetic carbon metabolism. This synthesis
provided a plausible explanation of the manifold interactions between
O2 and CO2 on the
photosynthesis of leaves.
In our model we linked equations describing Rubisco kinetics with
others on the stoichiometry of the photosynthetic carbon reduction
cycle and the photorespiratory carbon oxidation cycle, particularly on
their energetic (electron transport and ATP synthesis) requirements.
Building on the pioneering modeling of Hall, Tenhunen, Peisker, Laisk,
and others, we then drew together biochemical and organelle level
observations of the temperature dependencies of these phenomena, and
combined them with an empirical equation for the dependence of
"potential" electron transport rate on absorbed irradiance. Our
model attempted to match generalized observations of the photosynthetic
gas exchange of leaves with predictions from this mathematical summary
of photosynthesis.
We published our paper (8), "A biochemical model of photosynthetic
CO2 assimilation in leaves of
C3 species," in 1980. Susanne von Caemmerer
was, at that stage, a PhD student with Graham Farquhar at the Research
School of Biological Sciences, and Joe Berry had earlier been a visitor
to Barry Osmond's laboratory there. Many of the principles had been
discussed during the earlier visit, including what Joe Berry called the
"teeter-totter" (and Graham Farquhar called it a "see-saw")
between two flux limitations. That is, that photosynthesis cannot go
faster than a carboxylase activity limited rate, and also cannot go
faster than an electron transport limited rate, but should move easily
from one to another without the overall rate being much smaller than
either limitation-few "frictional" losses. A working model of
C3 photosynthesis including these principles was
developed before Joe Berry left, and this was integrated into the first
publication, a model of the C4 mechanism (2).
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WHY MODEL? |
Graham Farquhar was interested in modeling photosynthesis to
answer the question raised in his collaboration with Ian Cowan on
optimal behavior of stomata: What would the rate of
CO2 assimilation be if stomatal conductance were
slightly perturbed? Joe Berry was interested in how the
CO2-concentrating system of
C4 plants influenced CO2
fixation and photorespiration by Rubisco in the bundle sheath cells. In
both cases we needed a mechanism for representing the properties of
C3 plants in the context of a larger analytical framework. Susanne von Caemmerer, who came to this environment with a
degree in pure mathematics, used the model as a tool for making
quantitative links between leaf biochemistry and gas exchange kinetics (18).
Of course an underlying feeling was that one doesn't really understand
something until one can describe it mathematically. The model has been
subsequently used for pedagogic purposes, and also as a useful
framework for fitting to data, and then extrapolating. All this has
provided an interplay between model and measurement that has stimulated
development of both fields.
The interplay was also relevant to the direct issue of publishing our
paper. It was initially rejected: it contained no data, and it was
against Planta policy to publish papers that were solely models. Ian Cowan crafted a letter arguing that the modeled response curves were familiar to all the experimentalists who worked on gas
exchange. We are grateful to the Planta editors for
accepting the argument. Later Graham Farquhar was asked to referee all
modeling papers sent to Planta.
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BRINGING BIOCHEMISTRY AND GAS EXCHANGE TOGETHER |
The original model development was aided by breakthroughs in
understanding Rubisco oxygenase and oxygen inhibition of
CO2 fixation (12) and Rubisco kinetics and their
temperature dependence. It was also aided by developments in Rubisco
activation, but only in the sense of providing sufficient
activity to relate to rates in vivo. Understanding the pathway and
stoichiometry of the photorespiratory cycle was also important.
Improvements in gas exchange technology permitted measurement of
photosynthesis, stomatal conductance, and intercellular partial
pressure of CO2. Susanne von Caemmerer discusses
many of these issues in her recent text (17). Later, the pool sizes of
intermediates and enzyme activities were measured in relation to gas
exchange. The parametrization of our model requires estimates of
Rubisco kinetic constants and recently, plants with antisense to the
small subunit of Rubisco have proved an ideal system for measuring the
constants in vivo, as these plants are more completely Rubisco-limited
than the wild type. Some contemporary gas exchange measurements include
those of oxygen and its isotopes (17).
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CONTROL OF PHOTOSYNTHESIS |
Control of RuBP Regeneration
In our original model, RuBP regeneration was controlled by
electron transport, but could also be limited further by other components (lumped together) of the photosynthetic carbon reduction cycle. At higher [CO2], Tom Sharkey has drawn
attention to a third limitation that may come into play, that of triose
phosphate utilization. The details of all these interactions are yet to
be fully modeled. An interesting, new, and complex approach is being
taken by Agu Laisk who has been at the forefront of so much modeling of
photosynthesis. He and colleagues are developing a detailed model (13)
with dozens of enzymes and electron carriers so that regulation can be
examined, as well as control of overall leaf
photosynthesis. It could serve as a working encyclopedia of
what is known about enzymes, pathways, and membrane transport. It is
perhaps surprising that electron transport in whole-leaf models is
still treated largely empirically. Fluorescence studies have been
valuable in making progress. Engelbert Weis and Joe Berry (19) used our
model to relate the rate of CO2 exchange to that
of electron transport. This permitted a quantitative analysis of the
relation between fluorescence quenching properties and electron
transport. It separated the role of photochemical quenching and showed
that there is a residual role that could be related to
non-photochemical quenching. Bernard Genty and colleagues (11)
developed a model that has a theoretically satisfying basis and
simplicity, built on this finding. They showed that the quantum yield
of photosystem II is related to the ratio of steady-state fluorescence
to saturated fluorescence ( PS2 = 1  /m). The challenge remains that we still
don't know the physical mechanism of non-photochemical quenching.
Rubisco Activation and Its Control
Activation/carbamylation and inhibition of Rubisco are an active
area of research, experimentally and theoretically (17). Our original
model did not include these processes, and with the understanding of
that time their inclusion would have kept rates of photosynthesis below
those observed in real life. Susanne's thesis work (18) showed that to
achieve those rates with subsaturating [CO2],
Rubisco would have to be fully active. Few researchers were allowing
for subsaturation and the idea that Rubisco was a storage protein was
then wide spread. The subsequent work on tight binding of RuBP and of
inhibitors, and on carbamylation, has been an interesting case where
model formulation has informed the comparison of in vitro and in vivo data.
In the steady state, Rubisco activation is now generally thought to be
regulated and to place no greater limitation on photosynthesis than is
already there because of limited capacity for regeneration of RuBP
(typically electron transport). However, a low level of activation may
limit, for example, when light intensity suddenly increases.
Transients
Several groups have addressed the issue of transient changes in
light intensity and how such changes affect photosynthesis (14, 17).
The transients involve the times taken for stomata to respond, for
Rubisco activation to increase, and for the pool of phosphorylated
intermediates of the PCR cycle to autocatalytically build to the
appropriate level.
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REGULATION VERSUS LIMITATION: The Supply of CO2 to
Rubisco |
Limitations within the Leaf
Many earlier models of photosynthesis assumed that the kinetics of
CO2 assimilation were determined by resistances
to diffusion within the chloroplast. The biochemical models challenged
those views. Now the challenge is to modify the biochemical models with appropriate representations relating fluxes to concentrations. We need
three-dimensional parameters analogous to the one-dimensional concept
of resistance. Dave Parkhurst has made a start with more detailed
descriptions of diffusion within the intercellular air spaces of
leaves. There appears to be a significant drawdown in [CO2] from the substomatal cavities to the
sites of Rubisco, much of it presumably across the cell walls and
membranes, and an unknown contribution from the air spaces (17).
Limitations by Stomata
Chin Wong (20) showed that under many conditions where
photosynthetic capacity was caused to change, the ratio of
intercellular and ambient CO2 concentration
(Ci/Ca) often
remained constant, reducing with increasing leaf-to-air humidity
difference. Tim Ball and Joe Berry (1) generalized this finding and
effectively produced a succinct relationship between stomatal
conductance and rate of photosynthesis. When combined with a
biochemical model of photosynthesis, it has formed the basis for many
studies modeling whole-leaf and canopy carbon assimilation.
Ian Cowan described stomatal functioning in terms of optimization of
carbon gain with respect to water loss, with the free parameter being
tied to the statistics of rainfall (3). There is at present
insufficient information for a mechanistic model of stomatal functioning.
"Patchiness"
Heterogeneity in stomatal supply has been recognized as a problem
when it comes to assigning a concentration of CO2
at the substomatal level. If the heterogeneity of stomatal opening
comes about as the result of some imposed stress, one might be fooled into interpreting the data as a loss of photosynthetic capacity (16).
The current quantitative mapping of photosynthesis to address this
problem derives from analysis of chlorophyll fluorescence images (4).
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HOMOGENEITY OF LIGHT INTENSITY AND PHOTOSYNTHETIC CAPACITY |
We originally thought of our model as applying at the chloroplast
level and were somewhat surprised that it seemed to work for a leaf. It
assumed a homogeneous light environment, CO2
concentration, and concentration of Rubisco. It emerged later that the
same model should hold if light intensity and photosynthetic capacity
co-vary in space (7). Although that can happen within a leaf or canopy when light is averaged over a day (9), it does not hold in detail with
changes in light intensity on a time scale far shorter than that of
photosynthetic adaptation particularly a problem with light flecks
deep in a canopy. Thus big-leaf models with the total Rubisco per unit
ground area treated as a single leaf overestimate canopy
photosynthesis. Models that differentiate sun and shade leaves largely
overcome these problems (5) for broad-leaved species and grasses like
wheat. Nevertheless, there is a need to introduce penumbral effects,
especially for coniferous species. The analogous problem exists
considering the internal volume of a leaf as well.
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SCALING TO THE GLOBAL LEVEL |
Models of photosynthesis and stomatal conductance are becoming
embedded in larger models of the global carbon cycle and of land
surface feedbacks on climate. The physiological properties affect
atmospheric temperature and the hydrological cycle (10). Models now
strive to simulate the mass and energy balance of the land surface with
changing meteorological conditions over timeespecially in climate
models. Use of our model of photosynthesis has resulted in development
of theory to couple satellite remote sensing of spectral reflectance to
estimate the absorbed photosynthetically active radiation and
the efficiency of its use by chloroplasts at a global scale with
spatial resolution of about 1 km2. The coupling of these
with stomatal models has improved the simulation of heat and water
exchange between vegetated surfaces of continents and the atmosphere
(15). The significance for quantitative understanding of the
bioenergetics of our planet is just beginning to have an impact.
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MOVING TO LONGER TIME SCALES |
There is a need for longer-term modeling of photosynthesis. There
is little known about and thus little predictive modeling of how
Rubisco activity and electron transport capacity change with
environmental conditions. In practice most applications follow the
observed changes in leaf properties, either from direct observations or
from measurements of leaf nitrogen levels, as the latter often give
reasonable measures of capacity once the nitrogen tied up in cell walls
is accounted for (6). Future developments are inextricably linked with
modeling of growth and development and will necessarily involve
considerations of cell division and expansion and of hormonal and other
controls of gene expression.
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FOOTNOTES |
*
Corresponding author; e-mail farquhar{at}rsbs.anu.edu.au; fax
61-2-6249-4919.
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LITERATURE CITED |
-
Ball JT, Woodrow IE, Berry JA
(1987)
In
J Biggins, ed, Progress in Photosynthesis Research, Vol. IV. Martinus Nijhoff, Dordrecht, The Netherlands, pp 221-224
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Berry JA, Farquhar GD
(1978)
In
D. Hall, J. Coombs, T. Goodwin, eds, Proceedings of the 4th International Congress on Photosynthesis, Reading, England 1977. The Biochemical Society, London, pp 119-131
-
Cowan IR
(1986)
T.J. Givnish, ed, On the Economy of Plant Form and Function. Cambridge University Press, Cambridge, UK, pp 171-213
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Daley PF, Raschke K, Ball JT, Berry JA
(1989)
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Pearcy RW, Gross IJ, He D
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© 2001 American Society of Plant Physiologists
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TOP
A BRIEF HISTORY
WHY MODEL?