Estimation of the Relative Sizes of Rate Constants for
Chlorophyll De-excitation Processes Through Comparison
of Inverse Fluorescence Intensities
Regular Paper
Ichiro Kasajima1,2,4,∗, Kentaro Takahara1, Maki Kawai-Yamada2,4 and Hirofumi Uchimiya1,3
1Institute
of Molecular and Cellular Biosciences, University of Tokyo, 1-1-1 Yayoi, Bunkyo-ku, Tokyo, 113-0032 Japan
School of Science and Engineering, Saitama University, 255 Shimo-Okubo, Sakura-ku, Saitama City, Saitama, 338-8570 Japan
3Iwate Biotechnology Research Center, 22-174-4 Narita, Kitakami, Iwate, 024-0003 Japan
4Japan Science and Technology Agency (JST), Core Research for Evolutional Science and Technology (CREST), Saitama, 332-0012 Japan
2Graduate
The paper derives a simple way to calculate the linear
relationships between all separable groups of rate
constants for de-excitation of Chl a excitation energy. This
is done by comparison of the inverse values of chlorophyll
fluorescence intensities and is based on the matrix model
of Kitajima and Butler and on the lake model of energy
exchange among PSII centers. Compared with the outputs
of earlier, similar calculations, the results presented here
add some linear comparisons of the relative sizes of rate
constants without the need for F0′ measurement. This
enables us to regenerate the same alternative formula to
calculate qL as presented previously, in a different and
simple form. The same former equation to calculate F0′
value from Fm, Fm′ and F0 values is also regenerated in our
calculation system in a simple form. We also apply
relaxation analysis to separate the rate constant for nonphotochemical quenching (kNPQ) into the rate constant
for a fast-relaxing non-photochemical quenching (kfast)
and the rate constant for slow-relaxing non-photochemical
quenching (kslow). Changes in the sizes of rate constants
were measured in Arabidopsis thaliana and in rice.
Keywords: Arabidopsis thaliana • Chlorophyll fluorescence
parameter • Lake model • Relaxation analysis • Rice • Stern–
Volmer approach.
Abbreviations: EET, excited energy transfer; ∆Fv/Fm, decrease
of the parameter Fv/Fm during treatment; F, chlorophyll
fluorescence intensity (in general); Fm and Fm′, maximum
fluorescence intensities under dark-adapted or light-adapted
states; Fm″, maximum fluorescence intensity during relaxation
∗Corresponding
analysis; Fv/Fm, a chlorophyll fluorescence parameter estimating the maximal quantum yield of PSII photochemistry;
F0 and Fs, fluorescence intensities under dark-adapted or
light-adapted states; F0′, fluorescence intensity immediately
after turning off actinic light, with all PSII reaction centers
open; F0″, fluorescence intensity during relaxation analysis;
ke and ku, rate constants of qE quenching and unknown
quenching; IC, internal conversion; IS, intersystem crossing;
kf, kisc and kd, rate constants of chlorophyll fluorescence,
intersystem crossing and basal non-radiative decay; kfast and
kslow, rate constants of fast- or slow-relaxing nonphotochemical quenching; kNP, kfid and kNPQ, rate constants
of sum dissipation, basal dissipation and non-photochemical
quenching; kpi and kp, rate constants of photochemistry
under dark-adapted or light-adapted states; ksi and ks, rate
constants of the sum de-excitation under dark-adapted or
light-adapted states; LED, light-emitting diode; NPQ, a
chlorophyll fluorescence parameter estimating the size of
non-photochemical quenching relative to the size of basal
dissipation; PAM, pulse amplitude modulation; ΦFast and
ΦSlow, chlorophyll fluorescence parameters approximating
the quantum yields of qE quenching and unknown
quenching; ΦISC, a hypothetical chlorophyll fluorescence
parameter estimating the quantum yield of intersystem
crossing; ΦII, ΦNPQ and ΦNO, chlorophyll fluorescence
parameters estimating the quantum yields of PSII
photochemistry, non-photochemical quenching and basal
dissipation; PPFD, photosynthetic photon flux density; qL
and qP, chlorophyll fluorescence parameters estimating the
fractions of PSII centers in open states based on the ‘lake
author: E-mail, [email protected]/[email protected]; Fax, +81-3-5841-8466.
Plant Cell Physiol. 50(9): 1600–1616 (2009) doi:10.1093/pcp/pcp102, available online at www.pcp.oxfordjournals.org
© The Author 2009. Published by Oxford University Press on behalf of Japanese Society of Plant Physiologists.
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Plant Cell Physiol. 50(9): 1600–1616 (2009) doi:10.1093/pcp/pcp102 © The Author 2009.
Detailed calculation of chlorophyll fluorescence
model’ or ‘puddle model’ of PSII interactions; qPI, a chlorophyll fluorescence parameter estimating the size of photo-chemistry after treatment relative to the size of
photochemistry before treatment; qS, a chlorophyll
fluorescence parameter estimating the size of the sum deexcitation under light-adapted states relative to the size of
the sum de-excitation under dark-adapted states; qSlow, a
chlorophyll fluorescence parameter estimating the size of
slow-relaxing non-photochemical quenching relative to the
size of basal dissipation; S, sensitivity factor; S fluctuation,
the hypothetical fluctuation in the value of sensitivity factor
during measurement or treatment.
Introduction
Measurement of Chl a fluorescence parameters by the pulse
amplitude modulation (PAM) method provides information
about the de-excitation fluxes of Chl excitation energy
around PSII, by making non-destructive, simple measurements on almost any plant. Fluorescence parameters are calculated from several fluorescence intensities. The modulation
technique measures the increment of total fluorescence that
occurs in response to a measuring pulse. This method enables
measurement of fluorescence intensities, even under illuminated conditions. Fluorescence intensities are measured
under different light environments affecting the states of deexcitation fluxes around PSII (Baker 2008).
A typical measurement of Chl fluorescence with PAM is
illustrated in Fig. 1. The relative fluorescence intensity of a
dark-adapted plant is designated F0. F0 is considered to
reflect both the rate of photochemistry (i.e. the flux to photosynthetic electron transport) and the sum of the rates of
various basal non-photochemical de-excitations. Fm represents the relative fluorescence intensity of a dark-adapted
plant illuminated with a saturating pulse. A saturating pulse
completely reduces components of photosynthetic electron
transport for a moment and stops photosynthetic electron
transport, but it does not affect the non-photochemical deexcitations. Thus Fm reflects the rate of the basal non-photochemical de-excitation. The relative fluorescence intensities
under the illumination of a saturating pulse are conveniently
described as ‘maximum’.
Fs represents the relative fluorescence intensity of lightadapted plants which are illuminated with actinic light. The
quantum yield of photochemistry is decreased and the
quantum yield of non-photochemical de-excitation is
increased under illumination with actinic light. Under illumination, PSII shifts from an ‘open’ state to a partly ‘closed’
state, which means that some of the PSII reaction centers
cannot utilize excitation energy under illumination. The
increase of non-photochemical de-excitation caused by illumination has been usually referred to as ‘non-photochemical
quenching’. The difference between Fs and F0 is caused by
changes in the rates of these de-excitation mechanisms. The
relative maximum fluorescence intensity of a light-adapted
plant is called Fm′. The Fm′ reflects the rate of basal nonphotochemical de-excitation and the rate of induced nonphotochemical de-excitation. F0′ represents the relative
fluorescence intensity immediately after turning off the
actinic light. Supplemental, weak, far-red light to oxidize
photosynthetic electron transport fully is provided for a
moment before F0′ is measured. Thus F0′ reflects the rates of
dark-adapted photochemistry and of the light-adapted sum
non-photochemical de-excitation. Please note that F0′ is not
measured in Fig. 1. Fluorescence measurement in Fig. 1 was
performed with PAM-101, because its beautiful trajectory is
suitable for illustration. The fluorescence of several samples
was simultaneously measured with a Closed FluorCam in
the other experiments in this paper.
Kitajima and Butler (1975) presented a matrix model to
provide a linear explanation of fluorescence intensities by
the rate constants of the de-excitation mechanisms. This
matrix model satisfactorily explained the relationship
between the Chl fluorescence parameter Fv/Fm [ = (Fm – F0)/Fm]
and the quantum yield of photosynthetic electron transport.
Fv/Fm is now used as the parameter estimating the maximal
quantum yield of PSII photochemistry, which means the
quantum yield of PSII photochemistry in the dark. Since
Kitajima and Butler, conditional changes of photochemical
and non-photochemical quenching have been discovered
and measured with various Chl fluorescence parameters.
Although there are many parameters to measure various
properties of fluxes around PSII, for example as reviewed by
Roháček (2002), the explanation of the experimental results
is sometimes difficult because many of the parameters lack
formal theoretical definitions (Baker 2008).
Calculation based on Kitajima and Butler’s matrix model
is a powerful approach for developing Chl fluorescence
parameters which linearly quantify the relative amounts for
two groups of rate constants of de-excitation mechanisms.
Kramer et al. (2004) adopted this line of attack, generally
called the ‘Stern–Volmer approach’, and showed that the
relative amount of open PSII is estimated by a new parameter qL [= (Fm′ – Fs)/(Fm′– F0′) · F0′/Fs] instead of the commonly
used parameter qP. qL is favored rather than qP when the
‘lake model’ fits the situation better than the ‘puddle model’
of reciprocal exchange of Chl excitation energy among PSII
centers. In the lake model, all PSII centers are hypothesized
to be energetically connected with each other to exchange
Chl excitation energy. On the other hand, PSII centers are
hypothesized to exist as sole independent energy-processing
systems in the puddle model. Lake and puddle models are
the two opposite extremes. Although an intermediate model
between the lake model and the puddle model is consistent
with experimental data (Lavergne and Trissle 1995,
Lazár 1999), Kramer et al. (2004) gave a detailed discussion
and concluded that the calculated relative amounts of
open PSII are nearly equal between the lake model and the
Plant Cell Physiol. 50(9): 1600–1616 (2009) doi:10.1093/pcp/pcp102 © The Author 2009.
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I. Kasajima et al.
Fm″
Saturating pulse
Fm
Fluorescence intensity (a.u.)
Fm′
Fs
F0
Actinic light
0
F0″
Measuring pulse
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Time (min.)
Fig. 1 Illustration of fluorescence nomenclature and illumination conditions in PAM analysis. Chl fluorescence of a rosette leaf of Arabidopsis
thaliana was measured. In the figure, the x-axis represents the time-course of fluorescence measurement and the y-axis represents relative
fluorescence intensities. The measuring (modulation) pulse was turned on at 0.2 min. At 1.2 min, a saturating pulse was supplemented to measure
Fm. Fluorescence intensity just before this supplementation of a saturating pulse corresponds to F0. In addition to the measuring pulse, actinic
light at the photosynthetic photon flux density (PPFD) of 300 µmol m–2 s–1 was turned on at 2.0 min. During illumination with the actinic light, Fm′
and Fs were sequentially measured at 3.0, 4.0, 5.0, 6.0 and 7.0 min, then actinic light was turned off at 7.6 min. In the course of dark relaxation, Fm″
and F0″ were sequentially measured at 8.1, 9.1, 10.0, 11.0, 13.1 and 16.0 min, then the measuring pulse was turned off at 16.4 min.
intermediate model in terrestrial plants in which the reciprocal exchange of Chl excitation energy seems to predominate. Thus, calculation based on the lake model is a good
approximation to obtain insight into the sizes of de-excitation processes based on simple equations. For non-photochemical quenching, they showed that the parameter NPQ
(= Fm/Fm′ – 1) estimates the rate constant of induced nonphotochemical de-excitation relative to the rate constant of
basal non-photochemical de-excitation, by Equation (43) of
their paper. In addition to these calculations, they also
showed that the same formula of ΦII [= (Fm′ – Fs)/Fm′], which
estimates PSII photochemical quantum yield under illumination, can be derived from both the lake and the puddle
models. Parameters for the quantum yield of basal nonphotochemical de-excitation and induced non-photochemical
de-excitation under illumination were also derived {ΦNO = 1/
[NPQ + 1 + qL(Fm/F0 – 1)] and ΦNPQ = 1 – ΦII – ΦNO}. As apparent from the equations, the terms ΦII, ΦNO and ΦNPQ sum
to 1. This means that the total de-excitation fluxes of
Chl excitation energy can be linearly separated into
these three groups.
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Following the above calculations, Hendrickson et al.
(2004) proposed simple alternative formulae to calculate
ΦNO and ΦNPQ (they call ΦNO as Φf,D), such that ΦNO = Fs/Fm
and ΦNPQ = Fs/Fm′ – Fs/Fm. ΦNPQ consists of the same formula
as YN which was proposed by Laisk et al. (1997), thus providing a clear theoretical background for YN. The difference in
the ΦNO and ΦNPQ formulae between Kramer et al. (2004)
and Hendrickson et al. (2004) arises from the difference in
their choices of fluorescence intensities (whether or not F0′ is
used) and the different ways the formulae are derived. Values
derived from the two approaches are essentially the same,
thus calculations of YN [equal to ΦNPQ of Hendrickson et al.
(2004)] and of ΦNPQ by Kramer et al. (2004) give similar
values (Kramer et al. 2004).
Here, we propose an improved and easier way to calculate
the relative values of rate constants of de-excitation processes. We do this through a comparison of the inverse
values of the fluorescence intensities. Although the basic
hypothesis of our calculations is essentially the same as those
of previous calculations, the simplicity of our calculation
enables an improved understanding of the relationship
Plant Cell Physiol. 50(9): 1600–1616 (2009) doi:10.1093/pcp/pcp102 © The Author 2009.
Detailed calculation of chlorophyll fluorescence
between fluorescence intensities and the rate constants of
the de-excitation processes. Following our method, we are
able to calculate the relative amounts between the rate constants from only the fluorescence intensities F0, Fm, Fm′ and Fs,
without F0′. This elimination of F0′ from calculations is parallel to the results of Oxborough and Baker (1997), Hendrickson et al. (2004) and Miyake et al. (2009). Applications of our
calculations to photoinhibition are also described. Finally,
possible fluctuation of the S factor and its effect on the NPQ
value are discussed.
Results
The definitions of the de-excitation processes of Chl excitation energy and its names vary somewhat in the literature
and this can be very confusing. To minimize further confusion, we here modify those used in two recent papers on
linear calculations of the relative amounts of the rate constants (Hendrickson et al. 2004, Kramer et al. 2004) and we
create some new rate constants to make things clearer still.
The list of names and the relationships between the rate
constants is shown in Fig. 2.
First, we create the term ‘sum de-excitation’, which we
define as the sum of all the rate constants. This concept is
absent from previous analyses but is useful here as it will
help us to gain a better insight into the whole question. We
write the rate constant of sum de-excitation as ksi and ks,
where ksi represents the sum de-excitation of dark-adapted
plants and ks represents the sum de-excitation of lightadapted plants (‘i’ means ‘intrinsic’, as in kpi). Now, ksi (or ks)
has two components, photochemistry (kpi or kp) and sum
dissipation (kNP).
Here, the word ‘dissipation’ means ‘energy waste’ as the
definition of an English word. In terms of de-excitation of
Chl excitation energy, all de-excitation processes except for
photochemistry are energy-wasting processes. So, ‘dissipation’ could be equal to ‘non-photochemical de-excitation’.
To represent kNP, the word ‘sum dissipation’ is used instead
of ‘sum non-photochemical de-excitation’, because the
former phrase is shorter. This kind of philosophy was adopted
to determine the usage of seven words as to six specific deexcitation processes, and the results are listed in Table 1.
The word ‘quenching’ is generally used for de-excitation processes through intermolecular interactions. Thus ‘quenching’ is applicable to photochemistry and non-photochemical
quenching.
kNP is a rate constant, which is the sum of all rate constants for dissipation processes. Then kNP is further separated
into the sum of basal dissipation (kfid) and non-photochemical quenching (kNPQ). Basal dissipation is thought to consist
of Chl fluorescence (kf), intersystem crossing (kisc) and basal
non-radiative decay (kd) (Kramer et al. 2004). Induced nonphotochemical dissipation is hypothesized to consist of
three factors, ‘fast’, ‘intermediate’ and ‘slow’ components
based on the relaxation analysis (Quick and Stitt 1989).
Relaxation analysis represents the measurement of maximum fluorescence after switching off the actinic light. Fluorescence intensities measured in relaxation analysis are
referred to as Fm″ by Baker (2008). We adopt this usage of the
term Fm″ herein (illustrated in Fig. 1). Of the three factors of
non-photochemical quenching, the fast-relaxing component is often called qE quenching. qE quenching is dependent on the function of PsbS protein (Li et al. 2000). We
write the rate constant of qE quenching as ke, and the rate
constant of the sum of the other unknown non-photochemical quenchings as ku. In this paper, we also separate kNPQ into
the rate constant of fast-relaxing non-photochemical
quenching (kfast) and the rate constant of slow-relaxing nonphotochemical quenching (kslow). kfast and kslow represent
experimental approximations of ke and ku values. Of the rate
constants above, all except kfid, kf, kisc and kd are variable
according to the light intensity. In Fig. 2, we also summarized
the symbols for the quantum yields (Φ) of de-excitation
processes. As described in the Introduction, the quantum
yields of de-excitation processes are separated into three
parts, ΦII, ΦNO and ΦNPQ. ΦNPQ is further divided into ΦFast
and ΦSlow herein.
The de-excitation processes above are also correlated to
the Jablonski diagram of Chl energy states (Turro 1978, Dědic
et al. 2003, Heldt 2005, Sugimori 2008; Fig. 3). Chls at the
ground level (S0) are excited to the first singlet state (S1)
through absorption of red light or to the second singlet state
(S2) through absorption of blue light. Chls at the second singlet state are unstable and they lose energy in the form of
heat by internal conversion (IC) until the first singlet state is
reached. The excited Chl can return to the ground state
through IC or fluorescence emittance at the rate of kd and kf.
Energies of first singlet Chls can also be transferred to photochemistry or non-photochemical quenching at the rate of kp
(or kpi) and kNPQ. This kind of intermolecular process is called
as excited energy transfer (EET). Through intersystem crossing (IS), first singlet Chl can also be converted to the first
triplet state (T1), at a relatively low rate (kisc). First triplet
Chls return to the ground state through phosphorescence
emittance, IS or EET to form singlet oxygen of the ∆ state. In
Fig. 3, various rotation and vibration energy levels are omitted for the sake of simplicity.
Based on Kitajima and Butler’s matrix model under the
lake model of energy exchange among PSII centers, the following equation is hypothesized by Kramer et al. (2004):
F = S û kf / (kf + kd + kisc + kNPQ + kp) (generally)
(1)
Here, F represents the Chl fluorescence intensities in general and S is a constant. Equation (1) is written as a general
meaning, and for example the term kNPQ represents any
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I. Kasajima et al.
* Sum de-excitation (ksi or ks)
*
Photochemistry (kpi or kp ΦII)
* Sum dissipation (k
NP)
Basal dissipation (kfid ΦNO)
Fluorescence (kf)
Intersystem crossing (kisc)
Basal non-radiative decay (kd)
* Non-photochemical quenching (k
(a)
NPQ ΦNPQ)
* q E quenching (k )
e
* Unknown quenching (k )
u
(b)
* Fast-relaxing non-photochemical quenching (k
fast ΦFast)
* Slowly-relaxing non-photochemical quenching (k
k : rate constant
slow ΦSlow)
Φ : quantum yield
* : de-excitation processes with variable rate constants
Fig. 2 Nomenclature and components of de-excitation processes. The names of the de-excitation processes are shown. For grouped de-excitations,
its components are shown below, thus forming a tree-shaped view. The symbols of the rate constants and quantum yields are indicated in
parentheses. Two symbols each are shown for rate constants of sum de-excitation and photochemistry. The first symbol indicates the rate
constant in the dark-adapted state and the second symbol indicates the rate constant in the light-adapted state. Variable de-excitation processes
are indicated by asterisks. Two ways (a) and (b) of dividing non-photochemical quenching are shown; (a) represents conceptual division and
(b) represents the experimental division performed in this paper.
Table 1 Terminology of the de-excitation processes
De-excitation processes
Words
kpi
kp
Quenching
O
O
Dissipation
De-excitation
O
O
Photochemical
O
O
Non-photochemical
Basal
O
kf
kisc
kd
kNPQ
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
Induced
O
The applicability of three nouns (quenching, dissipation and de-excitation) and four adjectives
(photochemical, non-photochemical, basal and induced) was judged for six de-excitation processes. ‘O’
represents that the word is applicable to the specific process.
values of kNPQ including zero. This kind of general meaning is
also adopted in Equations (2) and (3). These general equations are used to show general relationships between fluorescence intensities and rate constants. The general equations
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should be looked at separately from the other specific equations, where terms are not shown when their values are zero
and specific fluorescence intensities are given. In all specific
equations, the same terms have the same values within a set
Plant Cell Physiol. 50(9): 1600–1616 (2009) doi:10.1093/pcp/pcp102 © The Author 2009.
Detailed calculation of chlorophyll fluorescence
IC
S2
IS
(k
isc
)
S0
EE
T
1O
2
IS
Phosphorescence
T1
Fluorescence (kf)
IC (kd)
Absorption (blue)
Non-photochemical
quenching (kNPQ)
S1
EET
Absorption (red)
Photochemistry (kpi or kp),
Chlorophyll
Fig. 3 Jablonski diagram of Chl energy states. S0, S1, S2 and T1 correspond to Chl energy levels in the ground state, in the first singlet state, in the
second singlet state and in the first triplet state. Arrows with solid lines indicate excitation processes through absorption of red or blue light.
Arrows with broken lines indicate de-excitation processes through internal conversion (IC), fluorescence and phosphorescence emittance,
intersystem crossing (IS) and excited energy transfer (EET). Every corresponding rate constant of de-excitation processes from the first singlet
state are shown in parentheses.
of calculations. Thus specific equations are used to calculate
the relationships between fluorescence intensities and rate
constants under each specific condition.
Equation (1) is also the fundamental equation in our
system. It is important that kp is written as kpi for the darkadapted state in specific equations. As described above,
values of kNPQ and kp change with light intensity. If presented
in simpler and the simplest terms, general Equation (1) is
equivalent to the following general equations, respectively:
F = S · kf / (kfid + kNPQ + kp) (generally)
(2)
F = S · kf/ks (generally)
(3)
The difference between general Equations (1) and (2)
occurs because we set the new rate constant kfid to represent
the sum of all basal non-photochemical de-excitations. The
rate constants of the denominator of the right side of Equation (2) represent three major groups of de-excitations.
In general Equation (1), ‘S’ represents the sensitivity factor,
which correlates with the instrument response (Resp) and
light intensity (I) to the fluorescence intensity (Kramer et al.
2004). However, the factor should also contain the proportion of incident light that is absorbed by the leaf (Aleaf) and
the fraction of absorbed light that is received by PSII (fractionPSII) (Baker 2008). The proportion of emitted fluorescence which is not re-absorbed by Chl (Unabs) should also
be included. Thus, at least five factors are included in S, the
sensitivity factor, in our system:
S = I · Aleaf · fractionPSII · Unabs · Resp
(4)
Other factors which can be included in S will be also discussed later in this paper. This equation should be applicable
to both direct detection and PAM detection of fluorescence
intensity. ‘I’ represents incident light intensity in direct
detection and measuring pulse intensity in PAM detection.
The factor S can fluctuate, especially under stressful conditions (Baker 2008). We refer to such fluctuation in S value as
‘S fluctuation’ in this paper. Because of the position of the
factor S in equations, S fluctuation causes complex effects on
the calculations. Therefore, we will for the moment hypothesize that there are no fluctuations in S during measurements as in the case of the previous calculations. Probable
effects of S fluctuation on Chl fluorescence parameters will
be discussed later in this paper.
Following general Equation (2) and based on the definitions of fluorescence intensities as described in the second
and the third paragraphs of the Introduction, the specific
equations below are derived for four representative fluorescence intensities F0, Fm, Fm′ and Fs:
F0 = S · kf/(kfid + kpi)
(5)
Fm = S · kf/kfid
(6)
Fm′ = S · kf/(kfid + kNPQ)
(7)
Fs = S · kf/(kfid + kNPQ + kp)
(8)
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Comparing these four equations, we notice that only the
left side and the denominators of the right side are different;
the other elements are all the same. So, to facilitate calculation, taking inverse values is the reasonable way, as follows:
F0–1 = (kfid + kpi)/(S · kf)
(9)
(16)
Using these six equations, the linear parameters already
described are readily interpreted by rate constants as:
Fv/Fm = (Fm – F0)/Fm = (F0–1 – Fm–1)/F0–1 = kpi/ksi
(20)
Fm–1 = kfid/(S · kf)
(10)
ΦII = (Fm′ – Fs)/Fm′ = (Fs–1 – Fm′–1)/Fs–1 = kp/ks
(21)
Fm′–1 = (kfid + kNPQ)/(S · kf)
(11)
NPQ = Fm/Fm′ – 1 = (Fm′–1 – Fm–1)/Fm–1 = kNPQ/kfid
(22)
Fs–1 = (kfid + kNPQ + kp)/(S · kf)
(12)
Next, both sides are multiplied by S · kf, and the sides
exchanged to obtain:
kfid + kpi = ksi = S ·
kf · F0–1
(13)
kfid = S · kf · Fm–1
(14)
kfid + kNPQ = S · kf · Fm′–1
(15)
kfid + kNPQ + kp = ks = S ·
kf · Fs–1
(16)
Now, because S · kf has a constant value under the present
hypothesis, from Equations (13)–(16) we can say that the
inverse values of the fluorescence intensities are proportional to the sum of all the rate constants. The left sides of
Equations (13)–(16) consist of four unknown rate constants
(kfid, kNPQ, kpi and kp) and the right sides consist of the
unknown, but stable, constant S · kf and four given fluorescence intensities (F0–1, Fm–1, Fm′–1 and Fs–1). From these equations, it is apparent that any of the four rate constants can be
represented as the multiplication of S · kf and addition/subtraction of inverse values of fluorescence intensities. Thus,
any relative amount between two of the four rate constants
or the addition/subtraction of the four rate constants can be
calculated quite simply. The following are the major equations for the calculation of relative amounts between rate
constants:
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kfid + kNPQ + kp = ks = S · kf · Fs–1
kpi = S · kf · (F0–1 – Fm–1)
(17)
kp = S · kf · (Fs–1 – Fm′–1)
(18)
kfid = S · kf · Fm–1
(14)
kNPQ = S · kf · (Fm′–1 – Fm–1)
(19)
kfid + kpi = ksi = S · kf ·F0–1
(13)
These photochemical–kinetic explanations are in accordance with the previous descriptions (refer back to the
Introduction). The situation is a little different for the parameter qL. In our system, qL is calculated as:
qL = kp/kpi = (Fs–1 – Fm′–1)/(F0–1 – Fm–1)
(23)
This formula is different from the formula provided previously by Kramer et al. (2004), which is:
qL = (Fs–1– Fm′–1)/(F0′–1 – Fm′–1)
= (Fm′– Fs)/(Fm′ – F0′) · F0′/Fs
(24)
This difference comes from the difference in the choice of
fluorescence intensities. Kramer et al. chose F0′ for calculation of kpi instead of F0. In our system, F0′ gives the following
equation:
kfid + kNPQ + kpi = S · kf · F0′–1
(25)
Taking Equation (15) from Equation(25) gives
kpi = S · kf · (F0′–1 – Fm′–1)
(26)
The qL of Kramer et al. is given by Equation (18)/Equation
(26).
Miyake et al. (2009) also derived an equation to calculate
qL without use of the F0′ value through several steps of calculations as follows:
qL = [ΦII/(1 – ΦII)] · [(1 – Fv/Fm)/(Fv/Fm)] · (NPQ + 1)
(27)
This equation can be transformed as follows:
qL = {[(Fm′ – Fs)/Fm′]/[1 – (Fm′ – Fs)/Fm′]}
· {[1 – (Fm – F0)/Fm]/[(Fm – F0)/Fm]} · (Fm/Fm′ – 1 + 1)
= [(Fm′ – Fs)/Fs] · [F0/(Fm – F0)] · (Fm/Fm′)
(28)
= [F0 · Fm · (Fm′ – Fs)]/[Fs · Fm′ · (Fm – F0)]
Both numerator and denominator of the right side are
divided by F0 · Fm · Fm ′ · Fs to obtain:
qL = (Fs–1 – Fm′–1)/(F0–1 – Fm–1)
(23)
Thus Equation (23) is the same as, and represents another
form of, the equation derived by Miyake et al. (2009).
Plant Cell Physiol. 50(9): 1600–1616 (2009) doi:10.1093/pcp/pcp102 © The Author 2009.
Detailed calculation of chlorophyll fluorescence
As shown above, our simplified system enables calculation of any relative amounts between the four rate constants
kpi, kp, kfid and kNPQ. Relationship between all rate constants
and fluorescence intensities can even be visualized under
various light intensities, as shown in Fig. 4A. Following our
approach, any new linear parameter to measure the relative
amounts between rate constants shown in Fig. 4A can be
derived, even for unprecedented combinations of rate constants. As an example, we propose a new parameter qS, which
is derived from Equation (16)/Equation (13) as follows:
qS = ks/ksi = F0/Fs
(29)
This simple parameter first enables estimation of the
changes in the rate constant of sum de-excitation.
Next, we take advantage of our system to separate kNPQ
into two components, kfast and kslow. It is proposed that factors of non-photochemical quenching can be distinguished
by relaxation analysis (Quick and Stitt 1989). Quick and Stitt
(1989) suggested fast, middle and slow components of
non-photochemical quenching based on relaxation analysis.
The half-times of dark relaxation of these components were
about 1 min, 5 min and hours. In relaxation analysis, the
time-course change of Fm″ is measured after the actinic light
is turned off for several minutes or longer in some cases. The
fast-relaxing component of non-photochemical quenching,
called qE quenching, is completely dependent on the function of PsbS (also called NPQ4) and qE quenching is completely lost in the npq4 mutant of Arabidopsis thaliana (Li
et al. 2000). In the course of dark relaxation of Arabidopsis
leaves, the wild-type and npq4 show approximately the same
Fm″ values after 1 min of relaxation and later on, judging from
the figures of the previous reports (Li et al. 2000, Li et al.
2002, Logan et al. 2008). The time of dark relaxation when
wild-type and psbS give similar Fm″ values is 5–7 min in rice
(Koo et al. 2004). When non-photochemical quenching is
divided into its fast, middle and slow components based on
the method of Quick and Stitt (1989), it seems to have been
empirically hypothesized that the pattern of a time-course
plot of Fm″ gives two straight lines corresponding to relaxation of the intermediate and slow components of nonphotochemical quenching (or three straight lines when the
A
S • kf • F 0-1
ksi
qS
ks
kpi
S • kf • F s-1
kp
qL
ΦNPQ
kNPQ
S • kf • F m-1
0
Φ II
kfast
kslow
Q
NP
ΦΝΟ
kfid
kfid
Dark
Light
B
S • kf • Fm′-1
S • kf • F m″ (1m)-1
S • kf • F m-1
Φ Fast
Φ Slow
S • kf • F 0″ (1h,5m)-1
S
• kf • F 0-1
S • kf • F 0″ (4h,5m)-1
kpi(0h)
S
0
• kf • F m-1
qPI
kpi(1h)
kpi(4h)
kslow
kfid
Before HL
(Dark)
q Slow
S • kf • F m″ (4h,5m)-1
kfid
kfid
HL (1 hr.)
(Dark-adapted)
HL (4 hr.)
(Dark-adapted)
S • kf • F m″ (1h,5m)-1
Fig. 4 Relationships among rate constants, Chl fluorescence intensities and Chl fluorescence parameters. (A) Relationships under dark-adapted
and light-adapted states. Except for the Chl fluorescence parameters, all values in the graph can be linearly compared (e.g. S · kf · F0–1 = kfid + kpi). qS,
qL and NPQ represent relative amounts between rate constants as indicated (e.g. qS represents the fractional change of the total rate constants).
ΦII, ΦNPQ, ΦNO, ΦFast and ΦSlow are each quantum yields of kp, kNPQ, kfid, kfast and kslow under light-adapted states. (B) Relationships in high-light
(HL) treatment of rice leaves. Values are shown for leaves before HL treatment and after HL treatment for 1 or 4 h.
Plant Cell Physiol. 50(9): 1600–1616 (2009) doi:10.1093/pcp/pcp102 © The Author 2009.
1607
I. Kasajima et al.
intervals of saturating pulses are short enough to detect the
change in the fast-relaxing component). This approach is
used in many papers. However, the relaxation plot gives an
even curve from 10 min through to 20 min of relaxation
analysis and this approach with straight lines does not seem
completely effective in our analysis of rice leaves (Fig. 5A).
The plot of NPQ during the relaxation analysis is even more
curvilinear (Fig. 5B). From these observations, we suggest
that the approach with straight lines is not necessarily accurate, at least in some situations. This is a natural consequence,
because there is no theoretical ground that the relaxation
pattern consists of straight lines. Next, we take an alternative
method. Even if the relaxation of non-photochemical
quenching is not linear or it does not follow any mathematically explainable curve, we can confidently estimate the size
of the non-photochemical quenching which relaxes within,
for example, 1 min in the dark because comparison between
the Fm′ value just before dark adaptation and that of Fm″ after
1 min of dark relaxation can give this value based on our
calculation system. We term the Fm″ value after 1 min of dark
relaxation Fm″ (1m). The rate constant for non-photochemical
quenching relaxing within 1 min of dark relaxation is termed
A
kfast, and the rest as kslow in our analysis of Arabidopsis. Alternatively, the rate constant kslow measured with the threshold
dark relaxation duration of 5 min is used in our analysis of
rice. The durations of ‘1 min’ of dark relaxation for Arabidopsis and of ‘5 min’ for rice are suggested just as examples and
can be modified according to the conditions and purposes
of the experiments. Similarly, this approach also does not
necessarily give a strictly correct division of non-photochemical quenchings, but this approach can strictly divide nonphotochemical quenchings into two parts which are relaxing
before and after a given duration of dark relaxation. Fm″ (1m)
gives the following specific equation in our system (please
note kNPQ = kfast + kslow):
kfid + kslow = S · kf · Fm′′(1m)–1
(30)
Equation (15) – Equation (30) gives kfast as follows:
kfast = S · kf · [Fm′–1 – Fm″(1m)–1]
(31)
Similarly, Equation (30) – Equation (14) gives kslow as
follows:
kslow = S · kf · [Fm″(1m)–1 – Fm–1]
(32)
B
1.20
1.80
light off
1.60
?
1.00
1.40
1.20
1.00
NPQ
Relative Fm value
0.80
0.60
0.40
0.80
0.60
0.40
light off
0.20
0.20
?
0
0
10
20
30
Time (min.)
0
0
10
20
30
Time (min.)
Fig. 5 Relaxation analysis with rice leaves. (A) Time-course measurement of Fm, Fm′ and Fm″ values. Leaf pieces were excised from the 3-week-old,
third leaves of rice cultivar Habataki. After dark adaptation and measurement of the Fm value, actinic light (PPFD = 1,500 µmol m–2 s–1) was
turned on. Fm′ values were measured during 5 min of illumination with actinic light, and then the actinic light was turned off. Fm″ values were
measured every 2 min during relaxation analysis for 30 min. Values are standardized with Fm values (the value at 0 min). The two broken lines
represent probable fits to the relaxations of middle and slow components, based on the method with straight lines. Data represent means and
SDs. n = 4. (B) Time-course calculation of NPQ values. NPQ values were calculated from data obtained in (A), and plotted vs. time. Data represent
means and SDs. n = 4.
1608
Plant Cell Physiol. 50(9): 1600–1616 (2009) doi:10.1093/pcp/pcp102 © The Author 2009.
Detailed calculation of chlorophyll fluorescence
Relationships of kfast and kslow with other rate constants
are also shown in Fig. 4A. In this way both kfast and kslow are
also able to be compared linearly with the other rate
constants.
Following the calculations above, the relative sizes of all
four groups of rate constants (kp, kfast, kslow and kfid) were
measured in rosette leaves of Arabidopsis under various light
intensities, where light intensities were measured by photosynthetic photon flux density (PPFD; µmol m–2 s–1) (Fig. 6A).
Values were standardized with the value of ksi (as 1.0). Interestingly, the sum de-excitation of the illuminated leaves
stayed at a relatively constant level, around 60% of that of
the dark-adapted leaves (in other words, qS was around 0.6)
under all light intensities examined. Under high light intensities, the size of kp decreases. To compensate for the decrease
of kp, non-photochemical quenching is induced. Especially
fast-relaxing non-photochemical quenching plays a major
role in keeping ks stable. In the conventional relaxation analyses, slow components of non-photochemical quenching
are called ‘qT’ and ‘qI’. ‘qT’ is induced even with low light
intensities and ‘qI’ is correlated with photoinhibition (Quick
and Stitt 1989). kslow in this paper approximately corresponds
to the sum of the rate constants of ‘qT’ and ‘qI’. In the experiment shown in Fig. 6A, actinic lights are supplemented only
for 5 min. Under this condition, ‘qI’ will be hardly induced
and ‘qT’ is expected to be the dominant component of kslow.
In fact, kslow is induced even with low light intensities such as
100 and 200 µmol m–2 s–1 in PPFD.
ΦII = kp/ks = (Fs–1 – Fm′–1)/Fs–1
(33)
ΦFast = kfast/ks = [Fm′–1 – Fm″(1m)–1]/Fs–1
(34)
ΦSlow = kslow/ks = [Fm″(1m)–1 – Fm–1]/Fs–1
(35)
ΦNO = kfid/ks = Fm–1/Fs–1
(36)
Here, the formula of ΦNO is the same as that of Hendrickson et al. (2004), and the sum of ΦFast and ΦSlow is the same
as ΦNPQ of Hendrickson et al. (2004) [ΦNPQ = Fs/Fm′ –
Fs/Fm = (Fm′–1 – Fm–1)/Fs–1], because the F0′ value is not used
both in this paper and in Hendrickson et al. (2004). The relationship between the different formulae of ΦNPQ and ΦNO of
Kramer et al. (2004) and Hendrickson et al. (2004) will be
discussed elsewhere in this paper. In Fig. 6B, quantum yields
of the two components of non-photochemical quenching
continued to increase as light intensity increased, in contrast
to the sequential decrease of ΦII under the higher light
B
1.00
1.00
0.80
0.80
Φ Slow
0.20
Φ NO
kfid
Photosynthetic photon flux density
( m mol m–2 s–1)
400
200
0
0
1400
1200
1000
800
600
400
200
0
0
1400
kslow
0.20
0.40
1200
kfast
Φ Fast
1000
kp
0.40
0.60
800
0.60
Φ II
600
Quantum yield
Relative sizes of rate constants
(fractional change from ksi)
A
As kNPQ was separated into kfast and kslow components, the
quantum yield of non-photochemical quenching, ΦNPQ, can
also be separated into ΦFast and ΦSlow, which correspond to
the quantum yield of de-excitation through fast- and slowrelaxing non-photochemical quenching. Quantum yields of
all four groups, ΦII, ΦFast, ΦSlow and ΦNO, were calculated
from data in Fig. 6A as follows, and the result is illustrated in
Fig. 6B:
Photosynthetic photon flux density
( m mol m–2 s–1)
Fig. 6 Illustration of rate constants and quantum yields under various light intensities. (A) Relative sizes of rate constants under various light
intensities. Twenty-four-day-old wild-type Arabidopsis (ecotype Col-0) was measured. Actinic lights were supplemented for 5 min. Values are
relative rate constants compared with the sum de-excitation under the dark-adapted state (PPFD = 0 µmol m–2 s–1). kp, rate constant of
photosynthetic de-excitation; kfast, rate constant of fast-relaxing non-photochemical quenching; kslow, rate constant of slow-relaxing nonphotochemical quenching; kfid, rate constant of basal dissipation. Data represent means and SDs. n = 4. (B) Quantum yields under various light
intensities. Quantum yields through each de-excitation processes were calculated from rate constants measured in (A), as shown in the text
[Equations (33)–(36)]. ΦII, quantum yield of photochemistry; ΦFast, quantum yield of fast-relaxing non-photochemical quenching; ΦSlow, quantum
yield of slow-relaxing non-photochemical quenching; ΦNO, quantum yield of basal dissipation. Data represent means and SDs. n = 4.
Plant Cell Physiol. 50(9): 1600–1616 (2009) doi:10.1093/pcp/pcp102 © The Author 2009.
1609
I. Kasajima et al.
conditions. At the highest light intensity (PPFD = 1,500 µmol
m–2 s–1), fast-relaxing non-photochemical quenching was
the prevalent pathway for de-excitation, followed by basal
dissipation, slow-relaxing non-photochemical quenching
and, lastly, photochemistry.
Finally, damage by high light was analyzed for indica and
japonica rice cultivars, based on our calculation system. Rice
varieties are separated into two subpopulations, indica and
japonica (Garris et al. 2005). From observation of several
varieties, it is reported that the decrease of Fv/Fm caused by
exposure to high light is less in japonica varieties than in
indica varieties. This decrease of Fv/Fm (∆ Fv/Fm) is thought to
reflect damage to PSII reaction centers because the content
of the D1 protein changes in parallel with the change of
Fv/Fm (Jiao and Ji 2001).
However, the question must be asked, does this decrease
in Fv/Fm actually reflect a decrease in the rate of photosynthetic electron transport? Fv/Fm represents the part of photochemistry in the sum de-excitation of dark-adapted leaves.
Because of its mathematical character [Equation (20)], there
are two possibilities that may be entertained as to the reason
for the decrease in Fv/Fm. The first is the decrease in photochemistry (kpi) and the other is the increase in slow-relaxing
non-photochemical quenching (kslow). Although leaves are
usually dark adapted for some minutes before measurements of Fv/Fm, the slow-relaxing non-photochemical
quenching is expected not to relax completely with this
treatment and this can accelerate the decrease in Fv/Fm.
Thus, the observed difference in ∆Fv/Fm between indica and
japonica rice cultivars cannot be readily attributed to the
difference in the damage to the photochemical apparatus.
Comparison of the effects of kpi and kslow on ∆Fv/Fm values
has been lacking till now because the effect of kslow has not
been considered and there has been no way to estimate the
changes in kpi. In our calculation system, the change of
the kpi value (qPI) and the change of the kslow value relative to
the kfid value (qSlow) are given by the following formulae,
which are similar to the case of qL and the NPQ calculations
in Equations (23) and (22):
qPI = [F0″(Xh,5m)–1 – Fm″(Xh,5m)–1]/(F0–1 – Fm–1)
(37)
qSlow = Fm″(Xh,5m)–1/Fm–1 – 1
(38)
In these equations, we introduced a new fluorescence
intensity F0″ to represent fluorescence intensity during dark
relaxation, which is measured without supplementation of
saturating pulse (as illustrated in Fig. 1). In the equations,
F0″(Xh,5m) represents the F0″ value after X h of high-light exposure and following 5 min of dark relaxation. The same is true
of the Fm″ values. The relationship between fluorescence
intensities, rate constants and fluorescence parameters
during high-light treatment of rice leaves is shown in Fig. 4B.
1610
To determine the change of qPI and qSlow values, we treated
rice leaves under high light (Fig. 7). Rice cultivars used in this
experiment were three indica cultivars (Kasalath, Habataki
and Nona Bokra) and four japonica cultivars (Nipponbare,
Koshihikari, Sasanishiki and Akihikari). Of these varieties,
the cultivar Kasalath, according to recent reports (Garris
et al. 2005, Kovach et al. 2007), belongs to a group called
aus, which belongs to the indica varietal group rather than
the japonica varietal group. Rice leaf pieces were excised
from fully expanded leaves and placed on water. F0 and Fm
values were measured after 5 min of dark adaptation and
every hour during exposure to high light (PPFD =
1,500 µmol m–2 s–1).
By exposure to high light, the Fv/Fm values decrease
(as can be seen, these are not strictly Fv/Fm, because the
leaves are not fully dark adapted). The ∆Fv/Fm value is significantly less in japonica leaves than in indica leaves, as reported
earlier (Fig. 7A; Jiao and Ji 2001). In a similar manner, qPI also
decreases after exposure to high light, and the decrease of qPI
is less in japonica than in indica, reflecting the tolerant nature
of japonica to high light (Fig. 7B). On the other hand, the
qSlow value increases after exposure to high light (Fig. 7C). In
contrast to the qPI value, the qSlow value is similar between
indica and japonica leaves for up to 3 h of exposure to high
light. After 4 h of exposure, the qSlow value is greater in japonica leaves than in indica leaves. At this time, the qSlow value is
similar between indica and japonica leaves, although the
value looks somewhat larger in japonica leaves. Hence, the
quite similar values of Fv/Fm between indica and japonica
leaves after 4 h of high-light exposure are explained by the
greater qPI and qSlow values in japonica leaves than in indica
leaves. Thus the previously observed slower degradation of
the photosynthetic apparatus by high-light treatment in
japonica leaves than in indica leaves was first examined by
the change of kpi values in this experiment. The pattern of
the change of kpi values was basically parallel to the change
of Fv/Fm values, although a difference in the change of qSlow
values also affected the difference in Fv/Fm values between
indica and japonica leaves after 4 h of high-light treatment in
this experiment. Judging from qPI values, about 30% of deexcitation capacity of photochemistry is lost after high-light
treatment for 1 h and about 45% of de-excitation capacity
of photochemistry is lost after high-light treatment for 4 h.
Such quantitative estimation of loss of de-excitation capacity of photochemistry was not possible with the conventional measurements with the parameter Fv/Fm. In general,
the quenching capacity of a quencher is approximately proportional to its concentration at low concentrations (Stern–
Volmer relationship). The quenching capacity becomes less
than expected by this linear relationship as the quencher
concentration becomes saturated. There are no data on
whether the concentration of the photochemical apparatus
of PSII in the thylakoid membrane is lower or higher than its
Plant Cell Physiol. 50(9): 1600–1616 (2009) doi:10.1093/pcp/pcp102 © The Author 2009.
Detailed calculation of chlorophyll fluorescence
0.35
A
indica
japonica
0.30
Fv /Fm
0.25
*
0.20
*
0.15
0.10
0.05
0
0 hr.
1 hr.
2 hr.
3 hr.
4 hr.
Exposure time
B
1.10
1.40
C
indica
japonica
1.00
0.90
indica
japonica
1.20
*
1.00
*
0.70
*
qSlow
qPI
0.80
0.60
0.80
0.60
0.40
0.50
0.20
0.40
0.30
0.00
0 hr.
1 hr.
2 hr.
3 hr.
4 hr.
Exposure time
0 hr.
1 hr.
2 hr.
3 hr.
4 hr.
Exposure time
Fig. 7 Change of parameters during high-light exposure. (A) Decrease of Fv/Fm. Leaf pieces were excised from the third leaves of each of two
individuals from three indica and four japonica varieties (so that n = 6 for indica and n = 8 for japonica). The decrease of Fv/Fm (∆Fv/Fm) was
measured during exposure to high light (PPFD = 1,500 µmol m–2 s–1). Leaves were dark-adapted for 5 min before each measurement. Data
represent means and SDs. Asterisks indicate significant differences between indica and japonica by Student’s t-test (P < 0.05). qPI values (B) and
qNP values (C) were also calculated from the same Fm and F0 values obtained in (A), and plotted vs. time. Data represent means and SDs. n = 6 for
indica and n = 8 for japonica. Asterisks indicate significant differences between indica and japonica by Student’s t-test (P < 0.05).
saturation level for this Stern–Volmer linear relationship. So,
for example, 30% loss of de-excitation capacity of photochemistry in PSII represents a loss of ≥30% of the functional
photochemical apparatus.
Discussion
In this paper, we derive a simple way to calculate relative
amounts between rate constants for the de-excitation
mechanisms of Chl excitation energy. Our results are complementary to some earlier calculations that deal with the
same issues (Hendrickson et al. 2004, Kramer et al. 2004,
Miyake et al. 2009). Here, let us also analyze the relationship
between our results and an earlier calculation which estimated the value of fluorescence intensity F0′ from Fm, Fm′ and
F0 values (Oxborough and Baker 1997). In their calculation,
the following equation is derived:
F0′ = F0/(Fv/Fm + F0/Fm′)
(39)
Oxborough and Baker (1997) observed a strong and proportional relationship between the measured F0′ value and
this calculated F0′ in several plant species. In Equation (39), Fv
represents Fm – F0. The right side of Equation (39) is transformed for comparison with our calculations. Fv in Equation
(39) is substituted by Fm – F0 to obtain:
F0′ = F0/[(Fm – F0)/Fm + F0/Fm′]
(40)
Fm · Fm′ is multiplied by both the denominator and numerator of the right side:
F0 ′ = F0 · Fm · Fm′/[(Fm – F0) · Fm′ + F0 · Fm]
= F0 · Fm · Fm′/(Fm ·Fm′ – F0 · Fm′ + F0 · Fm)
(41)
Both the denominator and the numerator of the right
side are divided by F0 · Fm · Fm′:
F0 ′ = 1/(F0–1 – Fm–1 + Fm′–1)
(42)
Plant Cell Physiol. 50(9): 1600–1616 (2009) doi:10.1093/pcp/pcp102 © The Author 2009.
1611
I. Kasajima et al.
Inverse values of both sides give:
F0′–1 = F0–1 – Fm–1 + Fm′–1
(43)
In our system, the left side of Equation (43) is expressed
with rate constants and the factor S using Equation (25) as:
F0′–1 = (S · kf)–1 · (kfid + kNPQ + kpi)
(44)
Similarly, the right side of Equation (43) is expressed with
rate constants and the factor S using Equations (9), (10) and
(11) as:
F0–1 – Fm–1 + Fm′–1 = (S · kf)–1 · (kfid + kpi – kfid + kfid + kNPQ)
(45)
= (S · kf)–1 · (kfid + kpi + kNPQ)
Because the right sides of Equations (44) and (45) are the
same, the left side of Equation (44) is equal to the left side of
Equation (45). Thus Equation (43) is also derived in our calculation system. This is a natural consequence, because the
background hypotheses are the same between our calculations and the calculation by Oxborough and Baker (1997).
Thus our calculation system is also consistent with the calculation by Oxborough and Baker (1997).
Similar to Oxborough and Baker (1997), exchangeability
between F0 and F0′ following Equation (43) can also be exemplified from the comparison between two different formulae
which calculate ΦNPQ. As described in the Introduction, the
formula for ΦNPQ of Kramer et al. (2004) [shown by Equation
(46) below] is different from that of Laisk et al. (1997) and
Hendrickson et al. (2004) (ΦNPQ = Fs/Fm′ – Fs/Fm). This difference occurs because the F0′ value is used in a part of the formula by Kramer et al. (2004). In Kramer et al. (2004), ΦNPQ is
given by the following equation:
ΦNPQ = 1 – ΦII – ΦNO
= 1 – (Fm′ – Fs)/Fm′ – 1/
[NPQ + 1 + qL · (Fm/F0 – 1)]
= Fm′–1/Fs–1 – [Fm′–1/Fm–1 + (Fs–1 – Fm′–1)/
(F0′–1 – Fm′–1) · (F0–1 – Fm–1)/Fm–1]–1
(46)
If F0′ in Equation (46) is substituted by the right side of
equation (43), ΦNPQ is calculated as:
ΦNPQ = Fm′–1/Fs–1 – [Fm′–1/Fm–1 + (Fs–1 – Fm′–1)/
(F0–1 – Fm–1) · (F0–1 – Fm–1)/Fm–1]–1
= Fm′–1/Fs–1 – [Fm′–1/Fm–1 + (Fs–1 – Fm′–1)/
Fm–1]–1 = Fm′–1/Fs–1 – Fm–1/Fs–1 = Fs/Fm′ – Fs/Fm
(47)
This equation is the same as that of Laisk et al. (1997) and
Hendrickson et al. (2004). Thus, the observed similarity
between ΦNPQ values calculated by two different formulae
with or without the F0′ value (Kramer et al. 2004) also shows
exchangeability between F0 and F0′ following Equation (43).
The two formulae for ΦNPQ are essentially the same under
the lake model, which is also true of two different formulae
for ΦNO presented by Kramer et al. (2004) and Hendrickson
et al. (2004).
1612
The comparison of inverse values of fluorescence intensities is not an entirely new approach. In inorganic chemistry,
the Stern–Volmer plot gives excellent linear correlations
between quencher concentration and its quenching capacity by plotting the inverse values of fluorescence intensities.
The essence of the Stern–Volmer plot is that an inverse plot
of fluorescence intensity gives linear quantification of
quenching capacities. In the analysis of the non-photochemical quenching of Chl fluorescence in plants, the basal dissipation is interpreted as the intercept of the Stern–Volmer
plot, and non-photochemical quenching is interpreted as
the variable term of the Stern–Volmer plot. The key output
of our paper represents a modification of the Stern–Volmer
approach to take an overview of a multiquencher system in
higher plants.
On the other hand, our calculations, like previous linear
calculations of rate constants in higher plants, are based on
the hypotheses that the reciprocal exchange of Chl excitation energy between PSII centers follows the lake model, and
that the ‘factor S’ remains constant throughout the measurement of Chl fluorescence. Although without strict
experimental support, the lake model does seem to fit with
the results of higher plant studies, at least so far (Kramer et al.
2004). Several other models have also been hypothesized
and tested especially regarding an explanation of the processes of fluorescence induction (or the Kautsky effect; Lazár
1999). We also have to question whether the assumption of
stability of the S factor is valid. We hypothesize that the
factor S consists of the product of five factors, where S = I ·
Aleaf · fractionPSII · Unabs · Resp. This resolution of factor S
may not be the final version yet, because secondary fluorescence and the inner filter are also expected to affect fluorescence intensity (Sušila and Nauš 2007). The low intensity of
fluorescence which is thought to be emitted from PSI may
also affect fluorescence intensity.
Of all these possible factors, an apparently varying factor
within a measurement is Aleaf (the proportion of incident
light that is absorbed by the leaf). The degree of light absorption by a leaf is adjusted by chloroplast movement both
positively and negatively. When absorption is accelerated
with weak blue light, the absorption ratio of a leaf can
increase by up to 15% depending on the species. Moreover,
these changes in absorption ratios are accompanied by
changes in fluorescence intensity (Brugnoli and Björkman
1992). Chloroplast movement also occurs under high-light
conditions in a different manner from that under low-light
conditions (Haupt and Scheuerlein 1990). Although a way to
avoid this fluctuation is to use Arabidopsis mutants which
are deficient in chloroplast movement (Kasahara et al. 2002),
the physiological properties of the mutants may be different
from the wild type; for example, mutants are more sensitive
to high-light stress. Also, this method is not readily applicable to other plant species. Chloroplast movement can occur
and influence the ratio of light absorption by a leaf within
Plant Cell Physiol. 50(9): 1600–1616 (2009) doi:10.1093/pcp/pcp102 © The Author 2009.
Detailed calculation of chlorophyll fluorescence
several minutes. When tobacco leaves are illuminated at a
high intensity, the intensity of transmitted light significantly
increases even after 5 min of treatment (Nauš et al. 2008). In
such cases, S fluctuation caused by chloroplast movement is
hypothesized.
Next, we will discuss a possible method to measure S fluctuation. If the measuring equipment is equipped with a farred light source, one can measure the sets of Fs, Fm′ and F0′
within short periods as illustrated in Baker (2008). These
fluorescence intensities give the following equations:
kfid + kNPQ = S · kf · Fm′–1
(15)
kfid + kNPQ + kp = S · kf · Fs–1
(16)
kfid + kNPQ + kpi = S · kf · F0′–1
(25)
From these equations, kp, kpi and ks are given by (16) –
(15), (25) – (15) and (16). From these rate constants, parameters ΦII and qL can be calculated within a set of Fs, Fm′ and F0′
measurements, but parameters relating to the non-photochemical quenchings are not calculated within a set of Fs, Fm′
and F0′ measurements because the Fm value is inevitably necessary to relate kfid to the rate constants of non-photochemical quenching, and these parameters such as NPQ remain
susceptible to S fluctuation.
The possible way to calculate changes in the factor S can
be derived from calculations. Following the method above,
kpi is calculated at any point in time without S fluctuation
as:
kpi = S ·
kf · (F0′–1 – Fm′–1)
(48)
If factor S changes from the initial non-fluctuated value
[designated as S(i) here] to a new, fluctuated value [designated as S(f) here], Equation (48) is written for each non-fluctuated and fluctuated condition as:
This relationship utilizes the stability of kpi, and the measurement should be under normal or weak light levels which
do not induce high-light damage in the PSII reaction center.
Of course this is a hypothetical model and so requires experimental verification before being established as an effective
method.
In a similar vein, we describe the hypothesis that
S fluctuation is one of the constituents of slowly relaxing
non-photochemical quenching. The possible influence of
chloroplast movement on quenching parameters was formerly discussed by Brugnoli and Björkman (1992). Because S
fluctuation is not actually dissipation, this effect is ‘pseudodissipation’. Let us hypothesize the case where S fluctuation
has occurred without any change in dissipations. Equation
(15) gives the following equations for both initial [S(i)] and
fluctuated [S(f)] S values:
kfid + kNPQ = S(i) · kf · Fm′(i)–1
(53)
kfid + kNPQ = S(f) · kf · Fm′(f)–1
(54)
kfid is given by:
kfid = S(i) · kf · Fm–1
Next, to see what happens, we calculate the parameter
NPQ under each initial and fluctuated condition. NPQ under
the initial condition is designated as NPQ(i) and NPQ under
the fluctuated condition is designated as NPQ(f) here. NPQ(i)
is calculated as:
NPQ(i) = Fm′ (i)–1/Fm–1 – 1
NPQ(i) = {(kfid + kNPQ)/[S(i) · kf]}/{kfid/[S(i) · kf]} – 1
= (kfid + kNPQ)/kfid – 1 = kNPQ/kfid
(49)
NPQ(f) is calculated as:
kpi = S(f) · kf · [F0′(f)–1 – Fm′(f)–1]
(50)
NPQ(f) = Fm′ (f)–1/Fm–1 – 1
S(i) · kf · [F0′(i)–1– Fm′(i)–1] = S(f) · kf · [F0′(f)–1 – Fm′(f)–1]
(51)
kf is deleted from both sides and both sides are divided by
the same terms to obtain:
S(f)/S(i) = [F0′(i)–1– Fm′(i)–1]/[F0′(f)–1 – Fm′ (f)–1]
(52)
(56)
By substituting Fm′(i)–1 and Fm–1 in the right side of this
equation with rate constants in Equations (53) and (55),
NPQ(i) is expressed by rate constants as:
kpi = S(i) · kf · [F0′(i)–1 – Fm′(i)–1]
F0′(i) in Equation (49) represents the F0′ value under the
initial state, and F0′ (f) in Equation (50) represents the F0′ value
under the fluctuated state. The same is true of Fm′ values.
Because the left sides of Equations (49) and (50) are the same
(kpi), the right sides are also the same:
(55)
(57)
(58)
By substituting Fm′(f) –1 and Fm–1 in the right side of this
equation with rate constants in Equations (54) and (55),
NPQ(f) is expressed by rate constants and S values as:
NPQ(f) = {(kfid + kNPQ)/[S(f) · kf]}/{kfid/[S(i) · kf]} – 1
= S(i)/S(f) · (kfid + kNPQ)/kfid – 1
= S(i)/S(f) · (1 + kNPQ/kfid) – 1
(59)
To compare the values of NPQ(i) and NPQ(f), kNPQ/kfid of
the right side of Equation (59) is substituted by NPQ(i) based
on Equation (57):
NPQ(f) = S(i)/S(f) · [1 + NPQ(i)] – 1
(60)
Plant Cell Physiol. 50(9): 1600–1616 (2009) doi:10.1093/pcp/pcp102 © The Author 2009.
1613
I. Kasajima et al.
NPQ(i) is subtracted from both sides to obtain:
NPQ(f) – NPQ(i) = S(i)/S(f) · [1 + NPQ(i)] – 1 – NPQ(i)
= [S(i)/S(f) – 1] · [1 + NPQ(i)]
(61)
Because NPQ(i) is ≥ 0, 1 + NPQ(i) is ≥ 1. Thus the positivity
or negativity of NPQ(f) – NPQ(i) is determined by the positivity or negativity of S(i)/S(f) – 1. An increase of S value caused
by S fluctuation results in a negative value of both S(i)/S(f) – 1
and NPQ(f) – NPQ(i), which means an increase of S value
during fluorescence measurement results in an apparent
decrease of the NPQ value. Alternatively, a decrease of the S
value during fluorescence measurement results in an apparent increase of the NPQ value.
The calculations above were about the time-course difference of the same sample. Then, what are the possible problems when comparing different plant samples? One possible
problem is the difference in Chl contents. Because light gradients in the sample are expected to vary according to Chl
contents, illumination at the same intensity can result in different light conditions between the samples with different
Chl contents, and result in different fluorescence intensities
(Sušila et al. 2004). In other words, leaves having a lower concentration of chloroplasts are more susceptible to light
intensities than other leaves, even if the conditions of the
chloroplast are the same between all leaves. Such leaves will
show lower ΦII values and greater NPQ values under
illumination.
When S values are not largely different between leaves,
and S fluctuation during measurement can be neglected,
comparison of the values of fluorescence parameters should
basically be valid. As demonstrated in this paper, all fluorescence parameters are ratios between rate constants, and the
effects of the S values are balanced out by divisions between
fluorescence intensities. A practical anxiety is that some
plants may be naturally stressed on the shelves of our greenhouses or in the field, and photochemistry may be naturally
lower by damage and ‘basal’ dissipation may be naturally
higher than their healthiest conditions because of slowrelaxing non-photochemical quenching which is induced
by the stress. Our unpublished data indicate a large induction
of slow-relaxing non-photochemical quenching by oxidative
stress. In fluorescence analysis, for example, higher values of
‘basal dissipation’ result in a lower NPQ value, because
NPQ represents the relative value of non-photochemical
quenching standardized with the value of basal dissipation.
Fluorescence, IS and IC originate from physicochemical characteristics of Chl a molecules, and do not seem to differ
between species of higher plants. At the moment, kfid could
be hypothesized as constant and the most reliable as the
internal standard in the comparison among higher plants, if
the plants are in a healthy condition. However, kfid is not necessarily a perfect internal control. There is no proof that
1614
there is no other de-excitation process involved in basal
dissipation, which can differ between plant species.
Finally, we discuss the probability of triplet Chl formation.
According to the Jablonski diagram of Chl excitation states
drawn in Fig. 3, the probability of creating triplet Chl is determined by the quantum yield of IS. The first triplet state is
reached after IS. As well as being de-excited by emitting
phosphorescence, this triplet Chl can also excite molecular
oxygen to a singlet state, which is very reactive and has a
damaging effect on cell constituents (Heldt 2005). The quantum yield of IS, ΦISC, is represented by the following
equation:
ΦISC = kisc/ks
(62)
Because kisc is not separable from kf and kd in fluorescence
measurements, ΦISC cannot be calculated by Equation (62).
Multiplication of kfid/kfid by the right side of Equation (62)
gives:
ΦISC = kisc/kfid · kfid/ks
(63)
kisc/kfid is a physicochemical parameter and should be
constant, and kfid/ks can be calculated by fluorescence intensities. Thus the probability of formation of triplet Chl can be
calculated if kisc/kfid is determined. Certainly, the absence of
basal dissipation other than kf, kisc and kfid is the prerequisite
for this calculation.
Thus based on the lake model of reciprocal exchange of
Chl excitation energy among PSII centers, our calculation
system provides a theoretical basis which can be applied
under various conditions to reach further estimations of the
metabolism of Chl excitation energy around PSII, as well
as providing additional hypotheses as to fluorescence
measurements.
Materials and Methods
Plant materials
Arabidopsis thalina (L.) Heynh. ecotype Col-0 was used in
this study. Seeds were germinated on Jiffy-7 peat pellets and
grown under continuous light (PPFD = 150 µmol m–2 s–1) at
23°C until the measurement of fluorescence. Seeds of rice
cultivars Habataki, Nona Bokra, Kasalath, Nipponbare, Koshihikari, Akihikari and Sasanishiki were obtained from the
Rice Genome Resource Center of the National Institute of
Agrobiological Sciences (Tsukuba, Japan). Rice seeds were
germinated at 28°C. Seedlings were transferred onto a nutrient-rich soil (Bon-Sol #1, Sumitomo Chemical, Tokyo, Japan)
and grown in a naturally lit greenhouse.
Measurement of Chl fluorescence with PAM-101
Chl fluorescence was measured using a PAM fluorometer
PAM-101 (Waltz, Effeltrich, Germany). After dark adaptation,
Plant Cell Physiol. 50(9): 1600–1616 (2009) doi:10.1093/pcp/pcp102 © The Author 2009.
Detailed calculation of chlorophyll fluorescence
the leaf was given a saturating pulse at 10,000 µmol
photon m–2 s–1 (KL 1500 LCD, Schott, Cologne, Germany).
After that, actinic light at 300 µmol photon m–2 s–1 was provided. Saturating pulses at 10,000 µmol photon m–2 s–1 were
also supplemented during illumination with the actinic light
and during dark relaxation.
Measurement of Chl fluorescence with FluorCam
Whole rosettes of Arabidopsis or excised leaves of rice
(approximately 0.5 cm2) which were floated on ion-exchanged water were measured. Leaves were dark adapted
for at least 1 h before starting measurements, and Chl fluorescence was measured with a Closed FluorCam (Photon
Systems Instruments, Brno, Czech Republic). Leaves were
also dark adapted for 5 min before each Fv/Fm measurement
in Fig. 7. Actinic lights were supplemented for 5 min before
measurements of Fm′ and Fs in Fig. 6. The light source of
actinic lights was red light-emitting diode (LED) light up to
PPFD = 200 µmol m–2 s–1 and white LED light from PPFD =
200 to 1,500 µmol m–2 s–1. There was no great difference
between fluorescence intensities measured with the same
intensities of red and white LED lights. Saturating pulses
were supplemented for 780 ms at the intensity of a PPFD of
approximately 6,000 µmol m–2 s–1 with white LED light.
Funding
The Ministry of Education, Culture, Sports, Science and
Technology, Japan; the Ministry of Agriculture, Forestry and
Fisheries of Japan; the Program for Promotion of Basic and
Applied Researches for Innovations in Bio-oriented Industry
(BRAIN).
Acknowledgments
Rice materials were kindly provided by the Rice Genome
Resource Center (RGRC) in the National Institute of Agrobiological Sciences (NIAS). We are grateful to Dr. Kintake
Sonoike for discussions. Dr. Keisuke Yoshida, Dr. Ko Noguchi
and Professor Ichiro Terashima kindly provided instructions
on measurement with the PAM-101 (trace of Fig. 1). We are
also grateful to them for discussions.
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(Received May 22, 2009; Accepted July 8, 2009)