ACPAtmospheric Chemistry and PhysicsACPAtmos. Chem. Phys.1680-7324Copernicus PublicationsGöttingen, Germany10.5194/acp-17-15045-2017Annual cycle of Scots pine photosynthesisHariPerttipertti.hari@helsinki.fiKerminenVeli-Mattihttps://orcid.org/0000-0002-0706-669XKulmalaLiisahttps://orcid.org/0000-0003-1775-8240KulmalaMarkkuhttps://orcid.org/0000-0003-3464-7825NoeSteffenhttps://orcid.org/0000-0003-1514-1140PetäjäTuukkahttps://orcid.org/0000-0002-1881-9044VanhataloAnnihttps://orcid.org/0000-0001-5523-905XBäckJaanahttps://orcid.org/0000-0002-6107-667XDepartment of Forest Sciences, University of Helsinki,
P.O. Box 27, 00014 Helsinki, FinlandDepartment of Physics, University of Helsinki, P.O. Box 64,
00014 Helsinki, FinlandDepartment of Plant Physiology, Estonian University of Life Sciences, Fr.R. Kreutzwaldi 1, 51014 Tartu, EstoniaPertti Hari (pertti.hari@helsinki.fi)20December2017172415045150537June20177July20171November201711November2017This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/This article is available from https://acp.copernicus.org/articles/17/15045/2017/acp-17-15045-2017.htmlThe full text article is available as a PDF file from https://acp.copernicus.org/articles/17/15045/2017/acp-17-15045-2017.pdf
Photosynthesis, i.e. the assimilation of atmospheric carbon to
organic molecules with the help of solar energy, is a fundamental and
well-understood process. Here, we connect theoretically the fundamental concepts
affecting C3 photosynthesis with the main environmental drivers (ambient
temperature and solar light intensity), using six axioms based on
physiological and physical knowledge, and yield straightforward and simple
mathematical equations. The light and carbon reactions in photosynthesis are
based on the coherent operation of the photosynthetic machinery, which is
formed of a complicated chain of enzymes, membrane pumps and pigments. A
powerful biochemical regulation system has emerged through evolution to match
photosynthesis with the annual cycle of solar light and temperature. The
action of the biochemical regulation system generates the annual cycle of
photosynthesis and emergent properties, the state of the photosynthetic
machinery and the efficiency of photosynthesis. The state and the
efficiency of the photosynthetic machinery is dynamically changing due to
biosynthesis and decomposition of the molecules. The mathematical analysis
of the system, defined by the very fundamental concepts and axioms, resulted
in exact predictions of the behaviour of daily and annual patterns in
photosynthesis. We tested the predictions with extensive field measurements
of Scots pine (Pinus sylvestris L.) photosynthesis on a branch scale in northern Finland. Our theory
gained strong support through rigorous testing.
Introduction
The movement of the globe around the sun generates a conspicuous annual
cycle of the solar radiation on the earth, and this cycle is especially
strong at high latitudes. Ambient temperatures respond to the cycle of solar
energy input and therefore a strong annual cycle exists also in temperature,
although a bit delayed. These large variations in light and temperature are
greatly influencing the distribution of plant species, especially in the
northern regions. As an example, Scots pines (Pinus sylvestris L.), while abundant all over
Europe, have also adapted especially well to the annual cycle of
radiation and temperature in the northern climate, forming even the treeline
in many regions (Juntunen et al., 2002).
As a consequence of the seasonal variation in light and temperature, many
perennials including deciduous trees have a strong metabolic annual cycle,
as they grow new leaves every spring that then become senescent in the
autumn. Temperature affects the timing of many phenological events, i.e. bud
burst and flowering (Hänninen and Kramer, 2007; Hari and Häkkinen,
1991; Linkosalo, 2000; Sarvas, 1972). However, the annual cycle is less clear
in coniferous trees, although they also have a period of intensive new
foliage growth in the spring and a specific time frame when old needles are
senescing in the fall.
The annual cycle of light and temperature is manifested in plant metabolism
in many ways. Actively metabolising cells are very sensitive to low
temperatures, and, as a consequence, they need to inactivate many processes
in order to avoid damage during winter in a process called winter hardening
(Hänninen, 2016). This means that the metabolism of, for example, evergreen
Scots pine needles also needs to follow a clear annual cycle. For example,
when sufficiently hardened, pine needles tolerate temperatures well below
-30 ∘C in winter; however, they are very sensitive to
temperatures below -10 ∘C during summer (Sakai and Larcher,
1987). The metabolism of photosynthesis recovers gradually from the winter
hardened state during spring, and the ambient temperature has an important
role in this recovery (Pelkonen and Hari, 1980).
Biochemically, photosynthesis can be defined as a long chain of action of
pigments, membrane pumps and enzymes, which use light as a source for energy
and atmospheric CO2 as source for carbon (see e.g. von Caemmerer and
Farquhar, 1981). Changes in the concentrations and activities of this
photosynthetic machinery generate the annual metabolic cycle of
photosynthesis. The physiological basis of the annual cycle at the level of
the synchronised action of the photosynthetic machinery is poorly known,
especially when it comes to the role of temperature in the synthesis,
activation, decomposition and deactivation of the machinery.
Sugars formed in photosynthesis are the source of energy for all cellular
metabolic activity and raw materials for growth. The length of the
photosynthetically active period is a key factor determining the annual
amounts of sugars formed in photosynthesis (Hari et al., 2013) and it plays
a very important role in the metabolism and growth of vegetation. Thus, a
theoretical understanding of the dynamics of the photosynthetic annual cycle
is key to understanding and explaining the growth of the trees growing at
high latitudes.
Physiological and biochemical research has provided useful knowledge of the
photosynthetic reaction chains, and the details of this machinery at the leaf,
organ and tissue levels have been intensively explored over decades, mostly
in controlled laboratory conditions (Farquhar and von Caemmerer,
1982; Farquhar et al., 1980; Kirschbaum et al., 1998; Laisk and Oja, 1998).
However, field measurements in mature trees are difficult to perform, and
the results are not easy to interpret. Therefore, the detailed physiological
knowledge that has mostly been obtained from laboratory experiments needs to
be translated into the field conditions, i.e. into trees living in their
natural environment to increase our understanding of the annual cycle of
photosynthesis under field conditions. This was our motivation in developing
a conceptual approach to the relationship of photosynthesis and the annual
variations in light and temperature.
The field of physics was facing a similar situation in the seventeenth century as field
studies on photosynthesis are encountering now. There were plenty of single
and scattered experiments and observations, but the unifying theory was
missing. Isaac Newton presented an approach to construct theories in his
book Principia Mathematica and unified the physical knowledge. He proceeded
in four steps when developing his theories, starting from the definition of
concepts and followed by the introduction of axioms. The mathematical
analysis of the behaviour of the system defined by the concepts and axioms
dominated his theory development. Finally, he derived predictions and tested
them. The new translation of Newton's famous book Principia Mathematica (Newton, 1999) clearly
presents these four steps.
In our previous analysis of photosynthesis taking place during midsummer, we
strictly followed Newton's example by introducing the concepts and axioms,
by analysing the behaviour of the system defined by these concepts and
axioms, and finally by deriving predictions and testing them (Hari et al.,
2014). However, it was evident that our theory omits the annual cycle of
metabolism and therefore it crucially fails to predict the photosynthesis in
the transitional times such as spring and autumn. The daily patterns of
measured and predicted CO2 exchange were quite similar, but the level
of predicted photosynthesis was too low, especially in early spring and late
autumn. We thus concluded that we have to introduce the annual cycle of
metabolism into our theory. Our aim is to develop our theory of
photosynthesis to cover the whole growing season and to explain and
predict the annual cycle of Scots pine photosynthesis in field conditions.
Theory development
The strong annual cycle of the solar light intensity and ambient temperature
is characteristic of the growing area of Scots pine: for example, Finland
has mostly a subarctic climate according to the Köppen–Geiger climate
classification (Peel et al., 2007), meaning that summers are quite mild,
with daily maximum temperatures being around 20 ∘C, whereas winters
are rather cold, with minimum temperatures often below -20 ∘C. A
regulation system has emerged through evolution to match the metabolism and cold
tolerance with the annual cycle of the solar radiation and temperature.
The process of photosynthesis consists of a large number of steps that form
the light and carbon reactions of photosynthesis. Each step is based on
actions of a specific molecule, with the most important being pigments (e.g.
chlorophylls and carotenoids), transmembrane proteins and membrane pumps
(e.g. ATPases), and Calvin cycle enzymes (e.g. ribulose-1,5-bisphosphate
carboxylase/oxygenase, Rubisco; Taiz et al., 2015). A proper functioning of the reaction chain in
photosynthesis requires that no single step is blocking the chain of
interlinked energy capture, membrane transport or synthesis of new
compounds. The core of pigment complexes as well as the membrane pumps and
enzymes are all proteins that have a tendency to decay (Araujo et al.,
2011; Hinkson and Elias, 2011; Huffaker and Peterson, 1974; Nelson et al.,
2014). Proteins are nitrogen-rich macromolecules (many contain
15–16 wt %N; Nelson et al., 2014) and they are costly to produce and maintain.
Therefore, it is natural that plants need to be able to use the limited N
reserves in an effective way. Since nitrogen has several competing usages in
metabolism, maintaining excess proteins is a “waste” of nitrogen.
The synthesis and decomposition of active protein molecules balance the
concentrations of active protein molecules in the photosynthetic chain.
Evidently, maintaining the proper balance of these molecules is a crucial
and demanding task for the metabolism of trees.
Large changes in the photosynthetic performance characterise the annual
cycle of photosynthesis, generated by changes in the concentrations of the
photosynthetic machinery. The maintenance of the proper concentrations of the
components in this machinery is taken care of by a very powerful biological
regulation system that has emerged through evolution to match the cellular
metabolism with the regular annual cycle of solar light and temperature and
is capable of modifying the processes within the normal range of conditions
but also provides sufficient resilience under sudden (short-term) extreme
conditions during the transition from winter to spring (Ensminger et al.,
2004a; Zarter et al., 2006). This system synthesises, activates, decomposes
and deactivates the critical photosynthetic machinery over timescales of
days (Nelson et al., 2014), and it is an acclimation system affecting
the activation and deactivation of transcriptional modules responsive to
light and temperature cues (e.g. Cazzonelli and Pogson, 2010; Toledo-Ortiz
et al., 2014). The changes in the machinery, in turn, generate changes in
the relationship between photosynthesis and light. This forms the metabolic
basis for our theory of the dynamics of the annual cycle of photosynthesis.
Definitions and axioms
We start our formulation with definitions as Newton did centuries ago. We
utilise physiological and physical knowledge in the formulation of the
axioms needed for the mathematical formulation.
Definition 1. The photosynthetic machinery is the complex web of pigments,
membrane pumps and enzymes forming the biochemical structure underlying
photosynthesis.
Plants are able to change the concentrations of active components in the
photosynthetic machinery.
Definition 2. Plants have a biochemical regulation system that synthesises,
activates, decomposes and deactivates the photosynthetic machinery.
The action of the biochemical regulation system generates the annual cycle
of photosynthesis and maintains the balance between the different steps in
the photosynthetic reaction chain. In this way, it generates a new property
in the photosynthetic machinery.
Definition 3. The state of the photosynthetic machinery is the emergent
property created by the actions of the biochemical regulation system
controlling the concentrations of active photosynthetic machinery.
The state of the photosynthetic machinery characterises the complex web of
energy capture, biochemical reactions and membrane transport in
photosynthesis with one single number. Next, we specify the action of the
biochemical regulation system on photosynthetic machinery.
Axiom 1. Synthesis and activation as well as decomposition and deactivation
of the photosynthetic machinery are changing the state of the photosynthetic
machinery.
Further, we specify the relationship between the environment and the synthesis
by the biochemical regulation system.
Axiom 2. The synthesis and activation of the photosynthetic machinery depend
linearly on the temperature above freezing point.
We also clarify the behaviour of decomposition and deactivation.
Axiom 3. The decomposition and deactivation of the photosynthetic machinery
depends linearly on the state.
Captured light energy may cause damage in chloroplasts in freezing
temperatures, when availability of CO2 is limited for the carbon
reactions in photosynthesis. This is why the biochemical regulation system
acts strongly to protect against damage.
Axiom 4. The accelerated decomposition and deactivation of the
photosynthetic machinery during cold and strong light depends linearly on
the product of light and temperature below freezing point.
The concentrations of the photosynthetic machinery affect the performance of
photosynthesis.
Definition 4. The efficiency of photosynthetic reactions is the capacity of
light and carbon reactions to synthesise sugars.
When we developed the theory of photosynthesis explaining the behaviour in
midsummer (Hari et al., 2014), we introduced an axiom stating that the
product of the saturating response to the photosynthetically active radiation
and CO2 concentration in the stomatal cavity determines the
photosynthesis at a point in space and time. Here, we introduce the annual
cycle of photosynthesis into the axioms with the efficiency of
photosynthetic carbon and light reactions and the efficiency photosynthetic
reactions replacing the parameter b in Eq. (1) in Hari et al. (2014).
Axiom 5. The photosynthesis rate at a point in space and time depends on the
product of two terms: (i) the efficiency of photosynthetic light and carbon
reactions and (ii) the product of the CO2 concentration in the stomatal
cavity and the saturating response of the light reactions to the
photosynthetically active radiation.
The state of the photosynthetic machinery determines the efficiency of
photosynthetic light and carbon reactions, which leads to our final axiom.
Axiom 6. The efficiency of photosynthetic light and carbon reactions depends
linearly on the state of the photosynthetic machinery.
Mathematical analysis
We introduce mathematical symbols to formulate the axioms in a more
exact and compact way. S denotes the state of the photosynthetic
machinery, f1 is the synthesis and activation, f2 is the
decomposition and deactivation, and f3 is the accelerated decomposition
and deactivation of that photosynthetic machinery (i.e. enzymes, membrane pumps
and pigments) caused by light at low temperatures.
Axiom 2 states that the relationship between the
synthesis and activation and temperature (T) is
linear above the freezing point, which gives
f1(T)=Max{a1T+Tf},
where Tf is the freezing temperature of needles
and a1 is a parameter.
According to Axiom 3, the relationship between the
decomposition and deactivation of the photosynthetic machinery and
the state of the photosynthetic machinery, S, is
linear:
f2(S)=a2S.
Accelerated decomposition and deactivation takes place to
protect the photosynthetic machinery against damage when
freezing temperatures hinder the carbon assimilation reactions of
photosynthesis (Axiom 4):
f3I,T=a3MaxTf-TI,
where I is the intensity of photosynthetically active radiation (PAR).
The synthesis, activation, decomposition and deactivation change the state
of the photosynthetic machinery as follows:
dSdt=f1-f2-f3.
Combining Eqs. (1)–(4), we obtain
dSdt=Max0,a1T+Tf-a2S-a3MaxTf-TI.
Equation (5) defines the state of the photosynthetic machinery at any moment
t when temperature and solar radiation records are available.
The photosynthesis rate, p, is obtained from Axiom 5 as follows:
p=EfICS,
where CS is the CO2 concentration in the stomatal cavity; f(I) is the
saturating response of the photosynthesis rate to the photosynthetically
active radiation (see Hari et al., 2014); and E is the efficiency of
photosynthetic carbon and light reactions which, according to Axiom 6, is as follows:
E=a4S.
When we developed the theory of photosynthesis in midsummer (Hari et al.,
2014), we introduced an axiom stating that the product of the saturating
response to the photosynthetically active radiation and CO2
concentration in the stomatal cavity determines the photosynthesis at a
point in space and time (A1 in Hari et al., 2014). When we quantified the
previous axiom with mathematical notations, we replaced the axiom A1 with
the new Axiom 5 that is quite similar to the previous one. The changing
efficiency of photosynthetic light and carbon reactions is the novel aspect
in Axiom 6. When we quantified the previous
axiom with mathematical notations, we introduced a parameter b (Eq. 1 in Hari et al., 2014). Equation (6)
is very similar to the previous Eq. (1) in Hari et al. (2014); the only
difference is that the efficiency parameter b is replaced with E, which is the
state-variable efficiency of photosynthetic carbon and light reactions. We obtain
the solution of the optimisation problem in the same way as in the analysis
of photosynthesis (p) during midsummer as follows:
p(I,E)=(uoptgmaxCa+r)a4Sf(I)uoptgmax+a4Sf(I),
where gmax is stomatal conductance when stomata are open,
Ca is the CO2 concentration in the ambient air, r is the rate of respiration and uopt
is the so-called seasonal modulated degree of optimal stomatal control given by
uopt=0,ifu≤0u,if0<u≤11,ifu>1,u=Ca-r/(a4SfI)λa(es-ea)a4Sf(I)gmax.
In Eq. (10), λ is a cost of transpiration, i.e. a measure of
water-use efficiency.
To summarise, Eqs. (5) and (7)–(10) predict the density of the photosynthetic
rate when we know the ambient temperature and solar radiation history,
density of photosynthetically active solar radiation, and concentrations of
water vapour and CO2 in the air. This prediction is clearly a dynamic
version of the formulation by Hari et al. (2014). The changing state of the
photosynthetic machinery (i.e. enzymes, membrane pumps and pigments)
determines the efficiency of light and carbon reactions, introducing the
annual cycle of metabolism into the prediction. Thus, the relationship
between light and photosynthesis changes smoothly during the seasons.
Parameter estimation
We tested the new theoretical prediction with field chamber measurements in
Scots pine trees in Lapland at the Värriö Subarctic Research Station
(SMEAR I; 67∘46′ N, 29∘35′ E; 400 m a.s.l.). We measured
the CO2 exchange of pine shoots with four branch chambers throughout
the year in 2011–2014 (Hari et al., 2014). In addition, photosynthetically
active radiation (I) was measured at each chamber, whereas the records for air
temperature, air humidity and CO2 concentration are site specific.
Despite the constant supervision, maintenance and malfunction of the
measuring system generated some gaps in the data. To obtain maximal data
coverage per year, we selected those chambers that measured over the whole
year without long maintenance and malfunction periods.
There are four parameters in Eqs. (5) and (7)–(10) that describe the
annual cycle of photosynthesis (a1, a2, a3 and a4). The
simultaneous freezing temperatures and sunny weather are quite rare events at our
measuring station, occurring only in early spring and very late in autumn. As
a result, the parameter a3 in Eq. (3) has a minor role in the
predictions and its estimation is based on very scarce data on the CO2
exchange with the accompanied environmental factors. The residual sum of
squares has several local minima, and they hamper the simultaneous estimation of
the parameters a1, a2 and a4. Therefore, we proceed stepwise;
first we fix the value of a parameter. Thereafter we estimate the values of
non-fixed parameters with standard numeric methods. We replace the value of
the fixed parameter with the one obtained in the estimation. We select
another parameter, fix its value with the one obtained in the previous
round of estimation and estimate the other two parameters again. We continue
the process of fixing, estimating and replacing for several rounds until we
get a reasonable fit. In this way, we find the smallest one from a large
number of local minima. The estimation resulted into the following values:
a1= 10, a2= 0.065 and a3= 2. The values of the
parameter a4 are year and chamber specific. We used a value of
-3 ∘C for Tf (T. Hölttä, personal communication, 2017).
Results
We predicted the state of the photosynthetic machinery, i.e. the annual state
of enzymes, membrane pumps and pigments with Eq. (5) using the measured
temperature and light intensity before the moment in consideration. The
predicted annual patterns of the state of the photosynthetic machinery were
quite similar between the different years (Fig. 1). There was, however, some
weather-driven variation. For example, the very warm August in 2014
generated the large peak in late summer.
The changes in the relationship between light and photosynthesis are
characteristic of our theory. Figure 2 depicts the daily patterns of the
measured and predicted leaf CO2 exchange early in the spring (Fig. 2a) and at
midsummer (Fig. 2b). The measured and predicted daily patterns generated by the
variation in light were very similar to each other, although the level of
photosynthesis increased considerably from spring to summer. Our theory
predicted the level of this increase during the summer successfully.
The annual pattern of the state of the photosynthetic machinery
(S, arbitrary units) during the years 2011–2014 in Finnish Lapland,
68∘ N.
Days of intermittent cloudiness dominate our northern climate in the summer
(Hari et al., 2014), giving rise to very strong within-day variations in the
light levels reaching the canopy. Our theory predicted strong variation in
photosynthesis during days of intermittent cloudiness, yet the measured leaf
CO2 exchange seemed to be very similar to the predicted one (Fig. 3a).
Heavy clouds tend to cover the sky during rainy days, strongly reducing the
light intensity. Our theory predicts strongly reduced photosynthesis during
dark rainy days. Again, the measured and predicted leaf CO2 exchanges
were very close to each other when thick clouds covered the sky (Fig. 3b).
Our theory predicts the clear effect of partial closure of stomata on sunny days
when the temperature strongly increases during the day. This type of days
is, however, a rather rare event at our northern measuring site.
Nevertheless, the measurements of leaf CO2 exchange showed a similar
pattern to our prediction on such days (Fig. 3c).
Measured and predicted leaf CO2 exchange during 2 days: (a) early in the spring (8 May) and (b) in
midsummer (18 July) in Finnish
Lapland, 68∘ N.
We have continuous measurements for four summers, consisting of more than
130 000 data points during each summer. The predictions of the leaf CO2
exchange of a shoot were very close to the measured pattern, without
exception. Also, the relationships between the measured and predicted leaf
CO2 exchange indicated close correlations between measurements and
predictions (Fig. 4). The predictions explained about 95 % of the
variance of the measured values.
The residuals, i.e. the difference between the measured and predicted leaf
CO2 exchange revealed only slight systematic behaviour (Fig. 5)
indicating that the theory was a quite adequate description of the
regularities in the photosynthesis of northern Scots pine.
Measured and predicted leaf CO2 exchange (a) during a day of
intermittent cloudiness (5 August), (b) during a cloudy day (22 July), and
(c) during a sunny day when the stomata close partially (7 July) in Finnish
Lapland, 68∘ N.
Discussion
Scots pine has a broad distribution range all over Europe, and the local
populations have adapted to the regular annual cycle of solar radiation and temperature.
The needle metabolism also has a clear annual cycle that
alternates between the cold tolerance and very low metabolic activity during
winter and the strong metabolism and cold vulnerability in summer. The annual
cycle is particularly strong in photosynthesis (Ensminger et al., 2004b;
Kolari et al., 2014; Öquist and Huner, 2003; Pelkonen and Hari, 1980).
We have worked decades with the annual cycle of vegetation from the analysis
of daily shoot elongation (Hari and Leikola, 1972; Hari et al., 1977), bud
burst of trees (Hari and Häkkinen, 1991) and photosynthesis
(Pelkonen and Hari, 1980). Our approach has been dynamic modelling without
a clear connection to the physiological background, although we were looking
for the metabolic explanations. The strong connection to the light and
carbon reactions and their basis on enzymes, membrane pumps and pigments is
the novel feature of our theory of the annual cycle of photosynthesis. It
provides sound physiological background to our concepts and axioms. We
utilised strongly physiological knowledge in the development of our theory.
Previously the focus has been in the mathematical formulation of the ideas,
whereas the physiological background has been quite unclear. The predictions
of our novel theory are close to those obtained previously
(Mäkelä et al., 2004) although the fit of the predictions with
measurements has improved considerably.
Relationship between the measured and predicted leaf CO2 exchange
in Finnish Lapland, 68∘ N in the year 2013. The dashed line represents
the 1:1
line.
The light and carbon reactions of photosynthesis are downregulated in
autumn in order to protect the sensitive machinery against low temperatures
and upregulated again in spring. This seasonality has been closely
connected to variations in ambient temperatures (Mäkelä et al.,
2004; Pelkonen and Hari, 1980) and photoperiod or light intensity changes
(Ensminger et al., 2004a; Porcar-Castell et al., 2008). A delayed effect of
temperature on photosynthesis recovery in spring is introduced
(Mäkelä et al., 2004; Pelkonen and Hari, 1980) and tested with
field measurements (Kolari et al., 2009).
The Newtonian approach provided a sound backbone to collect physiological
knowledge for the development of our theory of the annual cycle of
photosynthesis. The definitions of concepts determine the most important
features in the theory and the axioms the critical relationships between the
concepts. The application of the mathematical analysis and simulations of the behaviour of
the system, as defined by the concepts and axioms, proved to be an efficient
tool to analyse the consequences of photosynthesis and to derive
predictions.
We defined new concepts, the biochemical regulation system and the state of
the photosynthetic machinery (enzymes, membrane pumps and pigments) that played
a very important role in the argumentation and are justified from the basic
physiological understanding of the photosynthetic processes. Each step is
based on a specific pigment, membrane pump or enzyme. In an efficient
metabolic chain, the steps have to be in balance with each other. The
biochemical regulation system, with emerged through evolution, generates a balance
between the steps in photosynthesis, whereas its actions generate the
state of the photosynthetic machinery. The state of the photosynthetic
machinery determines the changing efficiency of the light and carbon
reactions in photosynthesis. In this way, the action of the biochemical
regulation system generates the annual metabolic cycle of photosynthesis and
the synchrony with the strong annual cycle of radiation and temperature.
The axioms clarify the action of the biochemical regulation system in
the synthesis and decomposition of the photosynthetic machinery. The physiological
basis of the actions is clear. Metabolic reactions take place faster at
elevated temperatures than at low ones. Thus, synthesis is temperature
dependent (Axiom 2). The enzymes, membrane pumps and pigments are non-stable
compounds as introduced in Axiom 3.
The residuals as a function of temperature and PAR in the year 2013
in Finnish Lapland, 68∘ N.
The increasing temperatures in the spring accelerate the synthesis and
activation of the photosynthetic machinery, resulting in increased
photosynthesis. The combination of sunny and cold mornings accelerates the
decomposition and deactivation and thus decreases photosynthesis. When the
spring proceeds, air temperature rises and the synthesis and activation
increase the state of the photosynthetic machinery, resulting in enhanced
photosynthesis.
The enzymes, membrane pumps and pigments are non-stable compounds, and,
consequently, their decomposition and deactivation increases during summer,
resulting in a quite stable state of the photosynthetic machinery. When
the temperature starts to decrease according to the annual cycle, the
synthesis declines, decreasing the pool of these non-stable compounds
resulting in a reduction in the light response of photosynthesis. In this
way the biochemical regulation system generates the annual metabolic cycle
of photosynthesis that is in delayed synchrony with the annual cycle of
radiation and temperature.
Our theory predicts a slow recovery in the spring, quite steady maximum in the
summer and slow decline in the autumn to be characteristic of the annual
cycle of photosynthesis due the synthesis, activation, decomposition and
deactivation of the photosynthetic machinery. The observed annual patterns
of photosynthesis are in good agreement with the above theoretical
prediction.
The diurnal cycle of radiation and temperature is clear in summertime and
missing during the polar night at our research site. However, we can omit
the polar night in photosynthetic studies due to darkness and low
temperatures. Our theory predicts that (i) photosynthesis during a day
follows the saturating response to light, since the changes in the
concentrations of enzymes, membrane pumps and pigments are so slow that the
changes do not affect the behaviour of photosynthesis during a day; and (ii) the action of stomata slows down photosynthesis during most sunny days. Our
field measurements are in agreement with this prediction.
Our theory has successfully passed the above qualitative tests. However,
quantitative tests are more severe and they can provide stronger
corroboration for the theory and show its universal character over a huge
number of environmental conditions and several seasons. We tested our theory
with field measurements over 4 years including over 130 000 measurements
of CO2 exchange, PAR, temperature, atmospheric CO2 and water
vapour concentration. Our theory predicted the annual and daily patterns of
photosynthesis explaining about 95 % of the variance in the measured
CO2 exchange, whereas residuals did not show any clear systematic
behaviour. Thus, our theory successfully passed the severe tests also in
quantitative terms. As a next step and proof of its universal nature, we
attempt to use the model developed for the branch scale to predict
ecosystem-scale fluxes in several Scots pine forests in different ecoclimatic regions
(see Hari et al., 2017).
The estimation of the parameter values is a challenge since the behaviour of
the residual sum of squares is very irregular and there are numerous local
minima disturbing the estimation with numeric methods. We therefore
developed a method that selected the smallest one from a large number of
residual sums of squares resulting in a quite stable solution of the
minimisation. Further analyses would benefit from independent data sets
from other sites in order to describe the variability in these parameters.
It is evident that the nitrogen availability (fertility) as well as plant
species affects the parameter a4; i.e. the higher the nitrogen
content in the leaves in general is, the higher the relationship between the
state of the photosynthetic machinery and the efficiency of photosynthetic carbon
and light reactions is (Eq. 7). On the other hand, parameter Tf
describing the temperature when the areas outside living cells freeze, is species specific and
also somewhat site specific depending on the water content (Sperling
et al., 2017). These events are rather rare but the sensitivity to such
events is reflected in parameter a3.
Short field campaigns and statistical analysis of the obtained data
dominates photosynthetic research under natural conditions. The often very
short and fragmentary measurement series hinder the studies of the annual
cycle of photosynthesis. The smoothly changing relationship between light
and photosynthesis is missing in most statistical analyses of field
measurements. The slow changes in the studied relationship are problematic
for the statistical analysis of field data and probably explain why there is
not any comparable ecological theory of the annual photosynthesis.
In conclusion, Scots pine has adapted to the regular annual cycles of light
and temperature and the effective biochemical regulation system of
the photosynthetic machinery has emerged through evolution. The action of the
biochemical regulation system generates the delayed annual cycle of
photosynthesis by synthesising, activating, decomposing and deactivating
enzymes, membrane pumps and pigments. The linear relationship between
synthesis and activation on temperature above the freezing point
synchronises the metabolic and light cycles with each other. Prevailing
light and the annual metabolic cycle determines photosynthesis, although the
action by the stomata modifies the photosynthetic response. Our extensive
field measurements corroborate the above conclusion.
All measurements at SMEAR I including the shoot chamber measurements
are available from https://avaa.tdata.fi/web/smart/smear/download. The code is available in
Mathematica and can be accessed via the corresponding author
(pertti.hari@helsinki.fi).
The authors declare that they have no conflict of interest.
This article is part of the special issue “Pan-Eurasian Experiment (PEEX)”.
It is not associated with a conference.
Acknowledgements
The research was funded by the Academy of Finland Centres
of Excellence programme (grants no. 1118615 and 272041), Academy of Finland
(277623), Nordic Centre of Excellence programme (CRAICC –
Cryosphere–Atmosphere Interactions in a Changing Arctic Climate), the Estonian Ministry of Sciences grant P170026 (Biosphere–atmosphere interaction and climate research applying the SMEAR Estonia research infrastructure), ERC
Advanced Grant no. 227463 ATMNUCLE, and the Nordforsk CRAICC-PEEX
Nordic–Russian Cooperation programme. We thank Pasi Kolari and the staff at
SMEAR I for the maintenance of the instruments and data.
Edited by: Martin Heimann
Reviewed by: Kalev Jõgiste and Kim Pilegaard
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