RESEARCH New Phytol. (2000), 145, 347–359
A mechanistic model of photoinhibition
H E L E N L. M A R S H A L L" , #*, R I C H A R D J. G E I D E R#
   K E V I N J. F L Y N N"
"Swansea Algal Plankton Research Unit, School of Biological Sciences,
University of Wales-Swansea, Singleton Park, Swansea SA2 8PP, UK
#Marine Biological Association of the UK, Citadel Hill, Plymouth PL1 2PB, UK
Received 17 May 1999 ; accepted 20 October 1999

A mechanistic model was developed, to simulate the main facets of photoinhibition in phytoplankton.
Photoinhibition is modelled as a time dependent decrease in the initial slope of a photosynthesis versus irradiance
curve, related to D1 (photosystem II reaction centre protein) damage and non-photochemical quenching. The
photoinhibition model was incorporated into an existing ammonium-nitrate nutrition interaction model capable
of simulating photoacclimation and aspects of nitrogen uptake and utilization. Hence the current model can
simulate the effects of irradiance on photosynthesis from sub-saturating to inhibitory photon flux densities, during
growth on different nitrogen sources and under nutrient stress. Model output conforms well to experimental data,
allowing the extent of photoinhibition to be predicted under a range of nutrient and light regimes. The ability of
the model to recreate the afternoon depression of photosynthesis and the enhancement of photosynthesis during
fluctuating light suggests that these two processes are related to photoinhibition. The model may be used to predict
changes in biomass and\or carbon fixation under a wide range of oceanographic situations, and it may also help
to explain the progression to dominance of certain algal species, and bloom formation under defined irradiance and
nutrient conditions.
Key words : photoinhibition, D1, model, reaction centre, quenching, photon flux density, quantum yield,
absorption cross section.

Recently, mathematical algal physiology models
have begun to focus on mechanisms of photoacclimation (Geider & Platt, 1986), nitrogen assimilation (Flynn & Flynn, 1998 ; Geider et al.,
1998), photoinhibition (Pahl-Wostl & Imboden,
1990 ; Eilers & Peeters, 1993), and may also include
vertical mixing (Cullen & Lewis, 1988 ; Kamykowski
et al., 1996), signifying a greater understanding and
appreciation of the importance of the acclimative
mechanisms employed by algae.
On the scale of phytoplankton generation time,
irradiance is highly variable because of factors such
as vertical mixing, cloud cover and flicker effect (due
to wave motion). Photosynthetic organisms acclimate to changes in irradiance via a variety of
mechanisms (Falkowski & Owens, 1980 ; Richardson
et al., 1983 ; Falkowski, 1984 ; Claustre & Gostan,
1987 ; Geider, 1987 ; Rivkin, 1990). Photoacclimation
may be achieved in a number of ways, but is
essentially accomplished by altering the efficiency
and capacity of the light reactions (light absorption
and photosynthetic electron transport) relative to the
*Author for correspondence (fax j44 (0) 1792 295447 ; e-mail
bdmarsha!swansea.ac.uk).
capacity of the dark reactions (CO fixation via the
#
Calvin cycle : see Richardson et al., 1983 for review).
Current models of algal physiology may include
photoacclimation (e.g. Flynn & Flynn, 1998 ; Geider
et al., 1998), but do not include a mechanistic
approach to photoinhibition. The photosynthesis
versus irradiance (PE) curve is central to these
models, using the equations of Jassby & Platt (1976).
These equations indicate the way in which the rate of
photosynthesis changes with irradiance for a given
physiological status. Modification of one of the
equations of Jassby & Platt (1976) allows the shape of
the PE curve to be described by three main
parameters (Geider et al., 1998), using parameter
names from Flynn & Flynn (1998) :
(1) α, the initial slope of the PE curve, which
represents the light harvesting efficiency of the
cell (g C g−" Chl a (µmol photon m−#)−")
(2) Chlq, the Chl a : C ratio, which represents the
size of the light harvesting apparatus (g Chl a g−"
C), and
(3) Pmax, the maximum rate of photosynthesis, where
carbon fixation is limited by the rate of the
photosynthetic dark reactions (related to the
activity of Rubisco) rather than the light harvesting ability of the cell (g C g−" C d−").
348
RESEARCH H. L. Marshall et al.
Table 1. The main features of photoinhibition
Event
Reference
1 Damage to D1 in PSII reaction centres is a linear function of
photon dose
2 D1 proteins are continuously turned over
3 The quantum efficiency of PSII is decreased by damaged D1
4 Non-photochemical quenching decreases the PSII specific effective
absorption cross section
5 Damaged D1 are stabilised in the thylakoid as 160-kDa
heterodimers, which perform a structural role
6 Excision of the 160-kDa heterodimers is the rate-limiting step in
repair
7 Damaged reaction centres provide protection from further
photodamage via non-photochemical quenching
8 Carotenoid\xanthophyll pigments provide non-photochemical
quenching, restricting further damage
9 Extent of inhibition depends on previous light and nutrient history
In addition, these models account for changes in
biomass (organic carbon and nitrogen), and pigment
content (Chl a), by including nutrient assimilation,
respiration and chlorophyll synthesis (Flynn &
Flynn, 1998 ; Geider et al., 1998).
Photoinhibition and photoacclimation are coupled
processes, and indeed the former must be countered
during the latter. While the phenomenon of photoinhibition has been studied for many decades, details
of the mechanisms have only been elucidated
relatively recently (Critchley, 1994 ; Baroli & Melis,
1996 ; Anderson et al., 1998). The main features of
photoinhibition are shown in Table 1 and are
discussed in the remainder of the introduction.
Photoinhibition of electron transport arises from
irreversible damage (termed photodamage) to the
D1 protein of photosystem II (PSII) reaction centres
(Adir et al., 1990 ; Falkowski et al., 1994). Photodamage does not suddenly begin at a given irradiance
but occurs whenever cells are illuminated (Adir et
al., 1990). The D1 protein is bound to the photooxidant P , and the primary electron acceptor
')!
pheophytin (Mayes et al., 1991), and as such, damage
to D1 has a probability of occurring every time there
is a charge separation between P and pheophytin
')!
(Baroli & Melis, 1996 ; Anderson et al., 1998). The
extent of D1 damage may however also be dependent
upon the presence or absence of oxygen (termed
acceptor side photoinhibition), with D1 damage
being increased in the presence of singlet oxygen
species (Durrant et al., 1990 ; Barber, 1995). Whether
or not the mechanism of photoinhibition is donor
side or acceptor side, at high photon flux densities
(PFD), charge separation occurs more frequently
and so the probability of D1 damage increases (Adir
et al., 1990).
D1 is a 32-kDa protein, and is situated alongside
a related 34-kDa form called D2. Damaged (i.e.
Adir et al. (1990) ; Hee Kim et al. (1993)
Adir et al. (1990)
Oquist et al. (1992)
Smith et al. (1990) ; Oquist et al. (1992) ;
Falkowski & Raven (1997)
Baroli & Melis (1996)
Baroli & Melis (1996)
Demmig & Bjorkman (1987)
Demmig & Bjorkman (1987)
Belay & Fogg (1978)
Prezelin & Matlick (1986)
inactive) reaction centres form a 160-kDa protein
which is a heterodimer complex of D2 and damaged
D1, as well as other breakdown products (Shipton &
Barber, 1992). The heterodimer complex provides
structural support for the inactive reaction centre
until the damaged D1 can be replaced (Tyystjarvi et
al., 1992). Only when the rate of damage exceeds
that of repair do these 160-kDa complexes (and
therefore non-functional PSII reaction centres)
accumulate in the thylakoids, and noticeable (i.e.
net) photoinhibition occurs.
Damaged D1 proteins are only excised from the
thylakoid if there is a replacement available, as the
heterodimer is needed to stabilize the associated
pigment antenna complex (Tyystjarvi et al., 1992).
The formation of the heterodimer complex is also
important for the degradation of damaged reaction
centres, because the conformational change provides
the target site for the highly specific proteinase
involved in the repair cycle (Aro et al., 1993). It has
been suggested (Adir et al., 1990) that in vascular
plants and green algae, part of reaction centre II
(RCII) acts as a photon counter in the same way as
the D1 protein. After receiving a certain number of
photons, part of RCII travels to the unappressed
regions of the thylakoid membrane where it binds
and stabilizes newly synthesized D1, then moves
back to PSII whereupon the 160-kDa heterodimer is
excised, and the functional D1 inserted. De novo
synthesis of D1 may be related to irradiance (Raven,
1989), the causal relationship is, however, unclear
and RCII migration might well be triggered by D1
damage itself and therefore not be directly related to
photon dose.
Newly synthesized D1 cannot be inserted into the
reaction centre until the damaged D1 has been
excised, because of the finite size of a reaction centre.
Excision has been proposed to be the rate-limiting
RESEARCH Photoinhibition model
step in the repair cycle (Baroli & Melis, 1996). The
presence of damaged D1 in the thylakoid provides a
non-photochemical quenching defence against
further photodamage (Oquist et al., 1992). Thus the
D1 repair cycle may be used to moderate the total
amount of damage sustained. This proposition is
supported by the fact that the D1 protein contains a
PEST gene sequence, common to proteins that are
under regulatory control and are rapidly turned over
(Critchley, 1994).
Photoinhibition is further complicated by a number of factors. There may be two main forms of PSII
in vivo, PSIIα and PSIIβ (Park et al., 1995). Park et al.
(1995) proposed that 25 % of PSII reaction centres
exist as PSIIα(possessing a large light harvesting
antenna), which are relatively more susceptible to
damage than PSIIβ. The ratio of these two forms was
thought to be independent of total antenna size (and
therefore of photoacclimative state). The loss of
PSIIα reaction centres, however, did not appear to
affect the quantum yield of PSII (Oquist et al., 1992 ;
Park et al., 1995), and thus may partially protect
PSII. The energy-dependent quenching provided
by these susceptible reaction centres (when
damaged) may protect PSIIβ reaction centres. This
‘ safety valve ’ of susceptible reaction centres also
allows the absorption cross-section of PSII to be
decreased quickly at high PFDs, by effectively losing
a relatively large area of light-harvesting proteins
without a subsequent decrease in the maximum
quantum efficiency of PSII. The inactivation of
PSIIβ reaction centres would however decrease the
quantum yield of PSII (Park et al., 1995). The
conclusion that two forms of PSII exist, however,
may be an artefact because electrons can be
channeled from the antenna of a damaged reaction
centre to that of an open one. Damaged reaction
centres might also be capable of re-emitting absorbed
energy, which may then be transferred to active
reaction centres (Raven & Samuelsson, 1986).
In addition to non-photochemical quenching
within reaction centres, non-photochemical quenching can also occur within the antennae and is
associated with pigments such as carotenoids (via the
xanthophyll cycle), and serves to protect Chl a and
other cellular molecules from photo-oxidation (Paerl
et al., 1983 ; Park et al., 1995). The quenching
performed by the xanthophyll cycle may allow
phytoplankton with these pigments to take advantage
of high irradiances. This was seen by Paerl et al.
(1983), who found that the progression of Microcystis
aeruginosa to dominance in a summer surface bloom
(with high PFDs), coincided with an increasing
carotenoid : Chl a ratio in the cyanobacterium. The
functioning of the xanthophyll cycle is associated
with the development of the trans-thylakoid pH
gradient and PSII reaction centre inactivation
(Rmiki et al., 1996), and so the quenching provided
by these pigments increases with increasing levels of
349
D1 damage (and therefore with PFD). Diadinoxanthin and diatoxanthin are the main components
of the xanthophyll cycle in diatoms and prymnesiophytes, however other algal groups posses different
β-carotene derivatives, which have the same role,
such as violaxanthin, antheraxanthin and zeaxanthin
(Rmiki et al., 1996).
Changes in pigment ratios (xanthophyll cycle) at
high PFDs have been found to decrease the effective
optical absorption cross section of PSII by as much
as 30 % (Sukenik et al., 1987), protecting PSII by
decreasing photon harvesting, although structural
changes in light harvesting centre II (LHCII), may
also have a role here (Sathyendranath et al., 1987 ;
Falkowski & Raven, 1997). The decrease in absorption cross section acts alongside D1 damage to
decrease the initial slope (α) of the PE curve (as α is
the product of the Chl a specific optical absorption
cross section (a*), and the maximum quantum yield
(φ m)).
A mechanistic simulation of photoinhibition is
presented here, which takes into account the physiological features already discussed. The model can
simulate photoacclimation and photoinhibition
under both steady-state and variable conditions,
during nutrient replete and depleted growth. It
should enable a more complete analysis of factors
affecting primary production and the physiological
mechanisms used by phytoplankters to acclimate to
different light regimes. The model is useful not just
as a predictive tool for photosynthetic production,
but also for clarification of the role of photodamage
in photoinhibition. Weaknesses in the structure or in
our ability to calculate parameter values for the
model indicate areas where more experimental work
is required.
 
The D1 damage and repair cycle (Fig. 1) forms the
basis of the mathematical model to be described.
Photoinhibition is modelled as a time dependent
decrease in α because of D1 damage, consistent with
conclusions from experimental work (Prezelin &
Matlick, 1986 ; Kana & Glibert, 1987 ; Weis & Berry,
1987). A list of model parameters and values is given
in Tables 2 and 4. Equations are listed in Table 3,
and throughout the text will be referenced using the
equation numbers stated in Table 3.
The photoinhibition model was incorporated
within the ammonium-nitrate interaction model
(ANIM) of Flynn et al. (1997). The simple photosynthesis component in ANIM was updated to that
of Flynn & Flynn (1998) (Eqn 1), and the chlorophyll
synthesis term was replaced with that of Geider et al.
(1998) (Eqn 2). However, the value of α in Eqn 1 is
now subject to modification because of the effect of
the D1 damage and repair cycle.
350
RESEARCH H. L. Marshall et al.
Table 2. List of definitions and units for parameters and variables used in the model
Variable\
parameter Definition
Gd
Kq
Lh
N-status
Pn
Chl a specific optical absorption cross section
Chl a specific initial slope of the PE curve
Slope constant for the dependence of non-photochemical
quenching on φ yield
Scaling factor enabling Qe to return a value between 1–0
Chlorophyll quota
Level of Chl a
Level of functioning D1 relative to the maximum level of
functioning D1
Level of damaged D1 present in the thylakoid relative to the
maximum level of damaged D1
Chlorophyll a synthesis rate
Correction term for differential susceptibility to
photodamage between species
Incident scalar irradiance
Slope constant for the dependency of φ yield on the relative
level of active D1
Gross D1 damage rate
Value of Q enabling half max. cell growth
Light history (i.e. photon dose of the previous hour)
Calculation of N-status (returns value between 1–0)
Value of Rn after changing the value of Ra to Pa
PS
Pmax
Pa
Carbon specific rate of photosynthesis
Maximum C-specific photosynthetic rate
Altered value of Ra
Q
Qo
Qe
Rep
RChl
Ra
Cell N : C quota
Minimum cell N : C quota
Antenna based non-photochemical quenching
Repair rate of damaged D1 in the thylakoid
Chl a degradation rate constant related to temperature
Normal parameter value
Rn
Value of a chosen model parameter given the value of Ra
S
Ucoeff
Sensitivity index
Normalizing factor giving C : N status as a value between
1–0
C-specific nitrogen uptake rate
Scaling factor for conversion of photon dose into damage
rate
Constant for the relationship between damaged D1 and the
repair rate
Constant for the relationship between damaged D1 and the
repair rate
Chl a synthesis regulation term
Quantum yield of photosynthesis
Maximum quantum yield
a*
α
B
C
Chlq
Chl a
D1
DD1
dChl
Ds
E
F
Vcn
X
Y
Z
ρChl
φ yield
φm
Units
m# g−" Chl a
m# g−" Chl a C−" µmol photon−"
d−"
Dimensionless
g Chl a g−" C
g Chl a L−"
Dimensionless
Dimensionless
h−"
d−"
µmol photons m−# s−"
Dimensionless
D1 D1−" photons−" m# h−"
g N g−" C
Photons m# h−"
Dimensionless
Units appropriate for parameter
test
g C g−" C d−"
g C g−" C d−"
Units appropriate for parameter
test
g N g−" C
g N g−" C
h−"
d−"
d−"
Units appropriate for parameter
test
Units appropriate for parameter
test
Dimensionless
Dimensionless
g N g−" C d−"
Dimensionless
Dimensionless
Dimensionless
Dimensionless
g C g−" C photon−"
g C g−" C photon−"
under
under
under
under
RESEARCH Photoinhibition model
a*
α
Table 3. Values for constants and parameter
initialization
Damage
Qe
φ yield
Active
D1
351
Damaged
D1
Repair
Fig. 1. Theoretical model of photoinhibition upon which
the mathematical model is based. Labels are defined in
Table 2.
Relationship between damaged D1 and φ m
The level of active D1 affects the photon harvesting
ability of PSII (α), such that α decreases alongside
active D1 (Park et al., 1995). This decrease in α is
due to the closure of reaction centres, which leads to
a decrease in the value of φ yield (Park et al., 1995).
A loss of up to 25 % of active D1 proteins has been
found not to decrease φ yield (Park et al., 1995). The
mechanism behind this is still unclear, but may be
because of the functional heterogeneity of PSII
reaction centres (Park et al., 1995), or to the
channelling of photons from damaged reaction
centres to functioning centres (Raven & Samuelsson,
1986). Although 25 % of active D1 may be lost
without a decrease in φ yield, after this threshold φ
yield decreases linearly with further decreases in D1
(Park et al., 1995). Therefore φ yield was modelled as
a threshold process using Boolean logic (Eqn 3) such
that it remains at the maximum value (φ m) until the
relative level of active D1 as a proportion of total D1
reaches 0.75 ; φ yield then decreases linearly with a
slope constant F.
Non-photochemical quenching
Formation of a trans-thylakoid pH gradient is due to
the build up of protons after a decrease in the
quantum yield of carbon fixation (Bjorkman &
Demmig-Adams, 1995). According to Bjorkman &
Demmig-Adams (1995), the level of Qe is linearly
related to excess photons. Excess photons are not
calculated in the model, so the quantum yield of
carbon fixation (Eqn 3) is used as a proxy, such that
Qe has a linear relationship with φ yield with a slope
constant B (Eqn 4). The scaling constant C in Eqn 4
allows Qe to vary between 0–1.
Antenna based non-photochemical quenching is
included in the calculation of the damage rate (Eqn
5) by reference to the parameter Qe (Eqn 4). Different
species can perform antenna based non-photochemical quenching to different extents ; however,
there are currently few data available with which to
model this species specificity. The correction factor
Ds was therefore included in Eqn 5 to simulate the
Constant\
initialization value
Value
Units
a*
B
Chlq
C
D1
DD1
Ds
F
Qo
Q
Ucoeff
Vcn
X
Y
Z
φm
0n00025
8
0n005
1
1
0
3n5
0n167
0n0588
0n17
0n5587
0n04
2i10−#&
1n163
0n552
0n125
m# g−" Chl a−"
Dimensionless
g Chl a g−" C
Dimensionless
Relative
Relative
d−"
Dimensionless
g N g−" C
g N g−" C
Dimensionless
g N g−" C d−"
Dimensionless
Dimensionless
Dimensionless
g C g−" C photon−"
differential susceptibility of different species to
photodamage.
D1 damage
The rate of D1 damage is modelled as a linear
function of photon dose (Eqn 5), in agreement with
the conclusions of experimental work (Adir et al.,
1990 ; Hee Kim et al., 1993). The relationship
between photon dose and D1 damage (represented
by the constant X in Eqn 5) was calculated from the
experimental results of Baroli & Melis (1996). Light
history was calculated over a period of 1 h, as this
accurately reproduced the results of Baroli & Melis
(1996). Using a light history term of 1 h produced
unsatisfactory model predictions, however, increasing the length of the light history term, as
suggested from the work of Ogren (1991), was found
to increase running time for the model without
significantly improving model predictions.
The damage rate is proportional to the relative
amount of active D1, such that the rate constant for
damage (the (X:Lh) term in Eqn 5) is decreased as
relative active D1 decreases, simulating the quenching provided by damaged D1. The protective effect
of Qe (Eqn 4) is achieved by subtracting Qe from the
damage rate (Eqn 5).
D1 repair
D1 repair consists of two processes, excision and
insertion. As the two processes are tightly coupled,
the rates of excision and insertion may be considered
as equal, and are modelled as such here (Eqn 6), in
that both processes are intrinsically included in the
repair rate.
352
RESEARCH H. L. Marshall et al.
Table 4. Equations used in the model
Eqn
no.
Equation
Description
0
α:E:Chl
1
1
Photosynthetic rate (g C g−" C s−"), regulated by the
physiological status and irradiance (E). From Flynn
& Flynn (1998).
Rate of Chl a synthesis (d−"). From Geider et al.
(1998).
1
PS l Pmax:tanh
2
dChla
ρChl:Vcn
l
kRChl :Chl a
dt
φc
3
φyield l (F:D1 Chl φm):(F:D1)j(F:D1φm):φm Regulation of φyield by the level of functioning D1 in
4
5
Qe l B:φyieldjC
Gd l (X:Lh):D1:DskQe
6
Rep l
7
N-status l
8
D1:
9
d
DD1: l DD1:(GdkRep)
dt
Change in the level of damaged D1 in response to the
D1 damage and repair cycle.
α l a*:(1kQ ):φyield
Regulation term for the initial slope of the PE curve
(m# g−" Chl a g−" C µmol photons−").
10
q
Pmax
0
q
Y:DD1
:N-status
ZjDD1
(QkQo)\(QkQojKq)
Ucoeff
d
l D1:(RepkGd)
dt
e
The repair rate constants (Y and Z in Eqn 6) were
calculated using the experimental results of Ohad et
al. (1984), which give levels of active D1 with and
without repair (using inhibitors to block protein
synthesis). As repair is triggered by (or in the same
way as) D1 damage (Adir et al., 1990), repair was
modelled as a function of the relative amount of
damaged D1 (DD1 in Eqn 9).
Repair cannot be a linear response to the level of
damaged D1, but must reach a maximum (Ohad et
al., 1984) otherwise net photodamage would not
occur. The maximum rate of repair was taken to be
equal to the rate of damage at the lowest irradiance
where net photoinhibition of photosynthesis was
evident. The repair rate was set to model a
hypothetical species which experiences net photodamage at 1000 PFD, and so the maximum rate of
repair is equal to the rate of D1 damage at 1000 PFD.
The model can however be set up to simulate net
photodamage at different PFDs via the alteration of
the constant Ds (Eqn 5).
As repair requires de novo synthesis of the D1
protein, the repair rate is decreased during N-stress
(Prezelin & Matlick, 1986). This is included in the
model by making the repair rate proportional to the
N-status of the cell (Eqn 7). The index for N-status
(Eqn 7), was taken from Flynn et al. (1999), and
returns a value between 1–0, where 1 represents
nitrogen replete growth. The rates of change of D1
and DD1 are thus given as functions of repair and
damage (Eqns 8, 9).
the thylakoids.
Antenna based non-photochemical quenching (h−").
Gross intrinsic damage rate of active D1 proteins (D1
D1−" h−").
Rate of repair of damaged D1 within the thylakoids
(D1 D1−" h−").
Normalized nitrogen status, returning a value between
1–0, where 1 is nitrogen replete. From Flynn et al.
(1999).
Change in the level of active D1 in response to the D1
damage and repair cycle.
Formulation of α
In Eqn 10, α is the product of the chlorophyll specific
absorption cross-section (a*), and φ yield (Eqn 3).
The a* is known to increase during a change from
sub-saturating to saturating PFDs because of a
decrease in self shading of pigments known as the
package effect (Herzig & Falkowski, 1989). As this
increase in a* is mainly associated with the pigment
changes during photoacclimation, it is not included
in the current model of photoinhibition. It should be
noted that the value of a* is species specific, and
must be modified when using the model to simulate
different species (Sathyendranath et al., 1987).
A decrease in a* has been found to occur with an
increase in PFD from saturating to inhibitory levels
(Kolber et al., 1988), which might be related to Qe.
This is included in Eqn 10 via the term (1kQe),
which decreases a* linearly with an increase in Qe
(Eqn 4). This is the simplest approximation of the
effects of Qe on a*, and experimental research is
required to elucidate the exact interaction between
these two factors.
  
Parameter sensitivity
Sensitivity analyses were performed using a single
parameter sensitivity index (Haefner, 1996). The
RESEARCH Photoinhibition model
353
effects of varying relevant parameters on the level of
active D1 were investigated (see Table 5 for response
indices and index calculation). Sensitivity index
values of 0 indicate no change in the level of active
D1 when the test parameter is varied. Values of 1
indicate a proportional change and values 1
indicate an increasing degree of sensitivity of the
response parameter to changes in the test parameter.
Values 1 indicate that a degree of certainty in the
correctness of the parameter value is required, as any
error in the test parameter could result in a large
error in the response parameter. Results of the
sensitivity analysis performed on relevant model
parameters are shown in Table 5. Values of S vary
between 0–4 showing that the model is generally
robust, and errors in parameter values will not
disproportionately affect model output.
D1 damage and repair rates
Direct observations of D1 damage are relatively
scarce, but fluorescence techniques are often used to
estimate the number of open-reaction centres. On
the assumption that the quencher of variable fluorescence is stoichiometrically related to the level of
active D1 in PSII (Ogren, 1991 ; Falkowski & Raven,
1997), fluorescence data are used here as well as data
on the level of active D1, to compare experimental
results with model output. In all comparisons of
model output with experimental results, the model
was set up to recreate the experimental method,
including all pre-conditioning light and nutrient
regimes.
A comparison of the level of functioning D1 with
increasing photon dose according to the experimental results of Park et al. (1995), and model
output, is shown in Fig. 2. In Fig. 3 daily changes in
the ratio of variable fluorescence, Fv\Fm are shown,
(data of Demmig-Adams et al., 1989), which are often
1.0
Relative functioning D1
0.8
0.6
0.4
0.2
0.0
0
1
Photon dose (mol photons m2 h–1)
Fig. 2. Relative amount of functioning D1 present with
increasing photon dose (non-steady state). Solid line shows
model predictions (correction factor, Ds l 0.6), circular
data points show experimental results redrawn from Park
et al. (1995).
used to assess the efficiency of PSII, alongside model
predictions for the change in active D1 (Ds l 1.2).
As shown by Figs 2 and 3, model predictions of
active D1 compare well with experimental results
measuring both active D1 itself and Fv\Fm ; however, Fv\Fm must be measured after a period of dark
relaxation to remove the rapidly relaxing components which are related to the functioning of Qe.
The model can also simulate experimentally
determined rates of D1 repair. The experimental
results of Ogren (1991), showing the time course of
recovery of Fv\Fm, are shown in Fig. 4 alongside
model predictions for the change in active D1 (Ds l
0.65).
The only parameter which must be adjusted to
simulate D1 damage and repair in different photo-
Table 5. Sensitivity analysis, showing the response of steady state levels of
D1 and Qe to changes in constants affecting the D1 damage and repair rates
Response index (S)
Constant
(normal value)
Ds (1n5)
B (8)
Y (1.163)
Z (0n552)
2
Test value
Active D1
Qe
2n5
3n5
4n5
7
9
0n581
1n744
0n276
0n828
0n367
0n205
0n134
1n189
0n853
3n901
0n623
k0n168
0n117
1n466
1n522
1n467
1n315
0n763
na
na
na
na
The index was obtained through model simulations of steady state growth,
where C : N l 6 and PFD l 1000 µmol m# s−". Unless stated otherwise Ds l
3.5. The analyses were performed using a single parameter sensitivity index
from Haefner (1996), where S l (RakRn\Rn)\(PkPn\Pn).
RESEARCH H. L. Marshall et al.
1.2
1.0
1.0
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0.0
0.0
1.0
0.8
0.6
Qe(h)
1.2
Normalized Fv/Fm
Relative functioning D1
354
0.2
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Time (d)
0.0
35
30
30
25
Fv/Fm
20
20
15
15
10
10
5
5
0
0
0
DD1/(D1+DD1)
Fig. 3. Comparison of experimental Fv\Fm results
redrawn from Demmig-Adams et al. (1989) (solid points),
with model predictions of the relative level of active D1
(continuous line) where the model was set up using the
same conditions as in the experimental method (correction
factor, Ds l 1.2).
25
0.4
1
2
3
4
Duration of recovery (h)
Fig. 4. Experimental results redrawn from Ogren (1991),
showing recovery of Fv\Fm after high light exposure
(solid circles), and model predictions (solid line) for the
decline in damaged D1 (correction factor, Ds l 0.65).
synthetic organisms is the parameter Ds, which here
is assumed to be related to the extent to which
different species can perform non-photochemical
quenching. Further research into this area is required, but the model’s behaviour suggests that D1
damage and repair rates (per photon received by D1)
might be universal, although the number of photons
received by D1 may be affected by the size of the
light harvesting apparatus and the presence of
accessory pigments.
Changes in Qe
The trans-thylakoid pH gradient on which Qe
depends is changed via the balance between the rate
of electron transport (increasing the gradient), and
ATP consuming processes which dissipate the build
0
500 1000 1500 2000 2500 3000 3500
PFD (lmol m–2 s–1)
Fig. 5. Experimental results redrawn from DemmigAdams et al. (1989), showing the increase in antenna based
non-photosynthetic quenching (Qe) with increasing photon flux density (PFD) (solid circles), and model predictions (solid line) (correction factor, Ds l 5).
up of protons (Bjorkman & Demmig-Adams, 1995).
The model uses φ yield to indicate the balance
between these two reactions. A comparison of model
output (Ds l 5) with the experimental results of
Demmig-Adams et al. (1989) for the level of Qe with
increasing PFD is shown in Fig. 5, and a close
correspondence can be seen between model output
and experimental data. Decreases in α are not only
associated with photodamage, but also with the
development of Qe (Demmig-Adams, 1990). As
already mentioned, the changes in Fv\Fm only
correlate well with the level of active D1 if a period
of dark adaptation is allowed to relax fluorescence
attributable to Qe, which relaxes in the dark within
minutes to hours (Demmig-Adams, 1990). From the
literature, 30 min would appear to be the average
time required to relax Qe, and in the model Qe also
returns to 0 within 30 mins under all light doses
which a phytoplankter might reasonably expect to
encounter in nature (maximum PFD l 2000 µmol
m−# s−").
N-limitation and\or starvation
The extent of photoinhibition is dependent upon
factors other than PFD, such as nutrient availability.
During nitrogen stress, the ability of a cell to repair
photodamage is decreased (as nitrogen is required
for the de novo synthesis of the D1 protein) and
therefore the level of damaged D1 is increased
leading to a decrease in φ yield (Prezelin & Matlick,
1986 ; Kolber et al., 1988 ; Herzig & Falkowski,
1989). During N-limitation, Isochrysis galbana shows
a decrease in the number of open PSII reaction
centres, accompanied by a decrease in φ yield and
RESEARCH Photoinhibition model
355
Photosynthesis (g C g–1 C d–1)
0.7
0.6
0.5
0.4
0.3
0.2
0.1
1.0
2000
0.8
1500
0.6
1000
0.4
500
0.2
0.0
0
0.3
0.0
0
500
1000
PFD (lmol m–2 s–1)
1500
2000
Fig. 6. Model output for a hypothetical species (correction
factor, Ds l 5), showing instantaneous rates of photosynthesis with varying N-status. C : N l 6 (solid line),
C : N l 9 (dotted line) and C : N l 13 (dashed line).
Pmax (Herzig & Falkowski, 1989). It was found that
a* might increase in N-limited cultures, but this may
be coupled with a decrease in the efficiency of
transfer of excitation energy from the antennae to
PSII reaction centres (Herzig & Falkowski, 1989).
Changes in the effective absorption cross section of
PSII (σPSII) are species specific, but generally
decrease with increasing PFD ; however, some
species (i.e. Thalassiosira weisflogii) may show no
change in σPSII at high PFDs (Kolber et al., 1988).
N-limitation has been shown to increase σPSII
(Kolber et al., 1988) ; this may be owing to a decrease
in pigment self shading (package effect), and is
dependent upon PFD (Herzig & Falkowski, 1989).
Model output PE curves for a hypothetical species
(Ds l 5), with varying degrees of N-stress are
shown in Fig. 6. It can be seen from Fig. 6 that the
model can recreate the effects of N-stress on
photoinhibition. In the model, Pmax decreases with
increasing C : N, as nitrogen is required for the
synthesis of Rubisco. It can also be seen that Nstressed cells (C : N l 13) show greater amounts of
photoinhibition, and show photoinhibition at lower
PFDs than N-replete (C : N l 6) cells. Although a*
is a constant in the model, the model can still
simulate changes in susceptibility to photoinhibition
due to N-stress. The model simulates the other
changes reported to occur during N-stress, such as a
decreased number of active PSII reaction centres,
decreased Chl a : C, and a decrease in Pmax (Pmax is
regulated by the ANIM part of the model). This
may be because although a* increases, decreases
occur in the efficiency of excitation transfer to PSII
reaction centres (Herzig & Falkowski, 1989), such
that changes in effective a* may be relatively small.
PFD (lmol m–2 s–1)
Relative photosynthesis (g C g–1 C d–1)
0.8
0.4
0.5
0.6
Time (d)
0.7
Fig. 7. Model output showing changes in the relative
photosynthetic rate (PS\Pmax, solid line) during a sinusoidal light regime (dotted line). Correction factor, Ds l 5.
Diurnal variation in PS
In nature, phytoplankton show a diel variation in
photosynthetic activity, with a high photosynthetic
rate in the morning, followed by an afternoon
depression (Sournia, 1974 ; Marra, 1980). The net
result is the generation of a hysteresis in the daily PE
curve (giving lower photosynthetic rates when
moving from high to low PFD compared with low to
high PFD). Various theories have been put forward
to account for this phenomenon ; the regulation of
Chl a content, endogenous rhythms (Prezelin &
Matlick, 1980), synchronous cell division (Paasche,
1968), regulation of metabolic priorities (Hind &
McCarty, 1973) and increases in photorespiration
(Beardall & Morris, 1975). According to Marra
(1978a), regulation of Chl a is unlikely to produce
the afternoon depression of photosynthesis as Chl a
content was found to be constant during the
depression, and the depression occurs even at subsaturating light intensities in the afternoon, when
Chl a regulation of the photosynthetic rate would be
expected to be greatest. Endogenous rhythms would
also seem an unlikely explanation, as the depression
can be removed when cells are exposed to a
fluctuating light regime instead of a diurnally varying
regime (Marra, 1978b). The depression of photosynthesis is distinct from photoacclimation (Post et
al., 1984), and may seem to mask it, but after
removal of diel variations, photoacclimation can still
be seen (Prezelin & Matlick, 1980).
The behaviour of the photoacclimation\inhibition
model developed here suggests that the in situ
afternoon depression of photosynthesis may be
attributed (at least to some extent), to a build up of
damaged D1 and Qe. Fig. 7 shows model output of
an instantaneous PE curve for a whole day (12 h
light), where changes in irradiance were simulated
using a sine function, thus simulating the irradiance
RESEARCH H. L. Marshall et al.
356
0.8
the conclusions from experimental work of Marra
(1978a), and showing that a given measurement of
photosynthetic production may not be independent
of previous measurements.
0.6
Light fluctuations
Photosynthesis (g C g–1 C d–1)
1.0
0.4
0.2
0.0
0
500
1000 1500 2000
PFD (lmol m–2 s–1)
2500
3000
Fig. 8. Model output showing the time dependence of the
photosynthetic rate (correction factor, Ds l 10) during Nreplete growth. The lines represent cells acclimated to a
sinusoidal light regime (12 h : 12 h, light : dark) with a
maximum photon flux density (PFD) of 2000 µmol m−# s−"
sampled at the beginning of the photoperiod. Instantaneous photosynthesis was then measured at a variety of
PFDs using different incubation periods (30 min, solid
line ; 1 h, dashed line ; 8 h, dotted line).
experienced by a phytoplankter held at the surface of
a stratified water column. It should be noted that
Fig. 7 does not represent separate incubations at
each light level, but represents continuous measurements of photosynthesis throughout the day, and
therefore the rate of photosynthesis at any given
PFD is affected by earlier rates. The photoinhibition
model of Eilers & Peeters (1993) produced similar
hysteresis curves between increasing and decreasing
PFDs. The supposition that the depressed rate of
photosynthetic production seen in the afternoon of a
24 h incubation is due to D1 damage and Qe could
additionally lead to the conclusion that shorter term
incubations (where a depression is also seen), may
similarly be linked to photodamage and protection.
However, this time dependence of the light saturated
rate of photosynthesis may not be only related to
photoinhibition.
Marra (1978b) suggested that in a sinusoidal
irradiance regime, the maximal photosynthetic rate
should occur at the beginning of the photoperiod,
with a time dependent decrease in the rate occurring
throughout the rest of the photoperiod, which may
or may not include photoinhibition (depending upon
the irradiance and nutrient status). After an initial
enhancement of the photosynthetic rate, it decays in
a time-dependent manner, thus differing incubation
times will produce different estimates of photosynthetic production at a given PFD (Marra, 1978a).
Fig. 8 shows model PE curves for incubations of
different length, and the time dependency of the
photosynthetic rate can be clearly seen, supporting
Vertical mixing is an important factor governing the
irradiance that a phytoplankter receives at any given
time, and many experiments have been performed to
investigate the acclimation of phytoplankton to
fluctuating light (Marra, 1980 ; Kromkamp &
Limbeek, 1993 ; Flameling & Kromkamp, 1997).
According to Marra (1980), it would be reasonable to
assume that because vertical mixing (and the associated irradiance change) is a phenomenon operating
within the generation time of algae, the algae would
have an acclimative strategy to optimize growth in
such a heterogeneous light environment. Fluctuating
light conditions because of vertical mixing, may
allow cells to take advantage of brief periods of high
irradiance at the surface of the water column, and
then to repair damage to the photosystem without a
corresponding decrease in the photosynthetic rate
when cells are moved to greater depths (thus
receiving lower irradiance).
There is some disagreement as to the response of
phytoplankton to fluctuating light regimes, which
would seem to indicate that different species acclimate to different extents during fluctuating irradiance (Flameling & Kromkamp, 1997). The
response is also highly dependent upon the frequency
of the fluctuations (Flameling, 1998). Integrated
daily photosynthetic production may be increased
(Flameling et al., 1998), equal to, or decreased when
cells are exposed to fluctuating light compared with
cells growing in a sinusoidal light regime (Yoder &
Bishop, 1985). Fig. 9 shows model predictions of
photosynthesis under a fluctuating light regime,
where the frequency of light fluctuations simulates
vertical mixing imposed on a normal diurnal light–
dark cycle (as used in Flameling & Kromkamp,
1997). As the peaks are symmetrical, it would seem
that the effects of photodamage are largely removed
by imposing a fluctuating light regime, supporting
the findings of Flameling & Kromkamp (1997). The
initial peak of PFD, however, produced a greater
photosynthetic rate than the final one (which was of
the same PFD). This was also seen by Marra (1980),
and may be owing to either an enhanced rate in the
initial peak, or to a depressed rate due to D1 damage
in the final peak.
Flameling & Kromkamp (1997) showed that if no
acclimation occurred during a fluctuating regime,
then daily-integrated photosynthesis would be lower
than in a sinusoidal regime. Acclimation to fluctuating light may involve decreases in cell size, Chl
a per cell and PSU size, and an increase in PSU
number (Flameling & Kromkamp, 1997). The photo-
357
1000
3.0
800
2.5
2.0
600
1.5
400
1.0
200
0.5
0
Photosynthesis (g C g–1 C d–1)
PFD (lmol m–2 s–1)
RESEARCH Photoinhibition model
0
0.3
0.4
0.5
Time (d)
0.6
0.7
Fig. 9. Model output showing the effect of a fluctuating
light regime (solid line), simulating vertical mixing, on
photosynthetic production (dotted line) for a hypothetical
species (correction factor, Ds l 5).
inhibition model was configured to simulate fluctuating and sinusoidal light regimes. Model output
predicted that Chl a : C decreased during fluctuating
light, and that given the same total daily light dose,
photosynthetic efficiency was higher in the fluctuating regime (0.634 mg−" C g−" C photon−") than in
the sinusoidal regime (0.485 mg−" C g−" C photon−"),
in agreement with the conclusions of Flameling &
Kromkamp (1997). Model behaviour also suggests
that whether or not daily-integrated photosynthesis
is greater in a fluctuating regime is dependent upon
whether the maximum PFD is saturating for photosynthesis. At subsaturating PFDs, photoinhibition is
not such an important factor, and the ability of cells
to take advantage of periods of high light, and then
repair the damage at low light, is not used. The
frequency of the fluctuations is important, as at high
frequencies, the time-dependent decay of the photosynthetic rate (due to Qe and D1 damage) may not
have a chance to depress photosynthesis greatly. The
reaction of the model also suggests that cells grown
in a fluctuating regime may have significantly greater
daily integrated photosynthetic production than
those in a sinusoidal regime, if the maximum PFD is
the same in both regimes (simulating a real oceanographic situation where a phytoplankter is either
held at the surface, or undergoes vertical mixing, but
still experiences the same maximum PFD at the
surface).
Bloom events
To predict bloom and succession events using
acclimation models, the photosynthetic and nutrient
uptake characteristics of different planktonic algal
species must be known (hence the photoinhibition
model was placed within a model capable of
simulating aspects of nutrient uptake). Photo-
inhibition becomes an important factor in predicting
primary productivity and\or bloom formation when
the water column is highly stratified with a low rate
of mixing. According to Steeman Nielsen (1962), the
maximum rate of photosynthesis is found at a depth
receiving c. 50 % of the surface illumination. If peak
surface irradiance is taken to be c. 2000 µmol m−# s−"
PFD, the depth at which blooms form should receive
a peak PFD around 1000 µmol m−# s−" PFD (this
may be a well defined layer in stratified water).
Important bloom forming species (i.e. Emiliania
huxleyi) do not exhibit noticeable photoinhibition
until 1000 µmol m−# s−" PFD (Nanninga & Tyrell,
1996), and so differential susceptibility to photoinhibition (combined with aspects of nutrient
acquisition), might explain the occurrence of speciesspecific blooms at particular depths in stratified
water, and also the competitive advantage of species
such as E. huxleyi (Nanninga & Tyrell, 1996), and
the freshwater alga Microcystis aeruginosa (Paerl
et al., 1983), at high PFDs. The consequences of
photoinhibition may thus account for the formation
of subsurface chlorophyll and photosynthetic
maxima (due to impairment of photosynthesis and
destruction of chlorophyll at the surface), whereas
deep chlorophyll maxima may be due to photoacclimation (an increase in cellular pigment levels
at sub-saturating PFDs).
Applicability of the model
One of the reasons for attempting the construction of
a mechanistic model is to focus attention on areas
lacking in experimental data. Further research is
required to investigate time dependence of the
photosynthetic rate, with the inclusion of D1
measurements to clarify the nature of the timedependent decay of light saturated photosynthetic
rates under low irradiance conditions. Investigation
is also needed regarding the role of accessory
pigments and their effects on a*. When more is
known about the capabilities of different species to
perform non-photochemical quenching via the xanthophyll cycle, the correction parameter Ds may be
removed and its role performed by the inclusion of a
variable maximum xanthophyll pigment pool size.
The size of the light harvesting apparatus is not
currently taken into account when calculating the
damage rate as the model calculates damage based on
incident rather than absorbed photons. Another
development of the present model therefore could
investigate the effects of the size of the light
harvesting apparatus.
Mechanistic models are useful in providing a way
of summarizing current research and drawing
together diverse aspects of algal physiology. Because
of the ‘ static ’ nature of experimental results, and the
fact that many data represent the net response to
stimuli, it is often unclear how different physiological
358
RESEARCH H. L. Marshall et al.
processes interlink in a dynamic way without an
explicit mathematical representation. Mechanistic
models, such as the inhibition model developed here,
allow a clearer overview of a number of processes,
including interactions between them, often clarifying
physiological mechanisms more easily than can be
done by undertaking a comprehensive review of the
often disjointed literature.
              
This work was enabled by a NERC CASE studentship to
H. L. M. from the Marine Biological Association of the
UK. Thanks to Dr Arnold Taylor and Dr H. Opik for
their helpful comments, support and advice.

Adir N, Shochat S, Ohad I. 1990. Light dependent D1 protein
synthesis and translocation is regulated by reaction center II.
Journal of Biological Chemistry 265 : 12563–12568.
Anderson JM, Park Y-II, Chow WS. 1998. Unifying model for
the photoinactivation of photosystem II in vivo under steady
state photosynthesis. Photosynthesis Research 56 : 1–13.
Aro EM, McCaffrey S, Anderson JM. 1993. Photoinhibition
and D1 protein degradation in peas acclimated to different
growth irradiances. Plant Physiology 103 : 835–843.
Barber, J. 1995. Molecular-basis of the vulnerability of photosystem II to damage by light. Australian Journal of Plant
Physiology. 22 : 201–208.
Baroli I, Melis A. 1996. Photoinhibition and repair in Dunaliella
salina acclimated to different growth irradiances. Planta 198 :
640–646.
Beardall J, Morris I. 1975. Effects of environmental factors on
photosynthesis patterns in Phaeodactylum tricornutum (Bacillariophyceae) II. Effect of oxygen. Journal of Phycology 11 :
430–434.
Belay A, Fogg GE. 1978. Photoinhibition of photosynthesis in
Asterionella formosa (Bacillariophyceae). Journal of Phycology
14 : 341–347.
Bjorkman O, Demmig-Adams B. 1995. Regulation of photosynthetic light energy capture conversion and dissipation in
leaves of higher plants. In : Schulze ED, Caldwell MM, eds.
Ecophysiology of photosynthesis. Berlin, Germany : SpringerVerlag, 17–47.
Claustre H, Gostan J. 1987. Adaptation of biochemical composition and cell size to irradiance in 2 microalgae – possible
ecological implications. Marine Ecology Progress Series 40 :
167–174.
Critchley C. 1994. D1 protein turnover : response to photodamage or regulatory mechanism ?. In : Baker NR, Bowyer JR,
eds. Photoinhibition of photosynthesis. Oxford, UK : BIOS
Scientific Publications, 407–431.
Cullen JJ, Lewis MR. 1988. The kinetics of algal photoadaptation in the context of vertical mixing. Journal of Plankton
Research 10 : 1039–1063.
Demmig-Adams B. 1990. Carotenoids and photoprotection in
plants : A role for the xanthophyll zeaxanthin. Biochimica et
Biophysica Acta 1020 : 1–24.
Demmig-Adams B, Adams WW, Winter K, Meyer A,
Schreiber U, Pereira JS, Kruger A, Czygan FC, Lange OL.
1989. Photochemical efficiency of photosystem II, photon yield
of O evolution, photosynthetic capacity, and carotenoid
#
composition during the midday depression of net CO uptake in
#
Arbutus unedo growing in Portugal. Planta 177 : 377–387.
Demmig B, Bjorkman O. 1987. Comparison of the effect of
excessive light on chlorophyll fluorescence (77K) and photon
yield of O evolution in leaves of higher plants. Planta 185 :
#
279–286.
Durrant JR, Giorgi LB, Barber J, Klug DR, Porter G. 1990.
Characterisation of triplet states in isolated photosystem II
reaction centres : oxygen quenching as a mechanism for
photodamage. Biochimica et Biophysica Acta 1017 : 167–175.
Eilers PHC, Peeters JCH. 1993. Dynamic behavior of a model
for photosynthesis and photoinhibition. Ecological Modelling
69 : 113–133.
Falkowski PG. 1984. Physiological responses of phytoplankton
to natural light regimes. Journal of Plankton Research 6 :
295–307.
Falkowski PG, Greene R, Kolber Z. 1994. Light utilisation and
photoinhibition of photosynthesis in marine phytoplankton. In :
Baker NR, Bowyer JR, eds. Photoinhibition of photosynthesis.
Oxford, UK : Bios Scientific publishers, 407–432.
Falkowski PG, Owens TG. 1980. Light–shade adaptation, two
strategies in marine phytoplankton. Plant Physiology 66 :
592–595.
Falkowski PG, Raven JA. 1997. Aquatic photosynthesis. London,
UK : Blackwell Science.
Flameling IA. 1998. Growth and photosynthesis of eukaryotic
microalgae in fluctuating light conditions, induced by vertical
mixing. PhD thesis, Catholic University of Nijmegen, The
Netherlands.
Flameling IA, Kromkamp J. 1997. Photoacclimation of Scenedesmus protuberans (Chlorophyceae) to fluctuating PPFD simulating vertical mixing. Journal of Plankton Research 19 :
1011–1024.
Flameling IA, Wyman K, Falkowski PG. 1998. Growth and
photosynthesis of Thalassiosira weisfloggi in fluctuating light
conditions. In : Flameling IA. Growth & photosynthesis of
eukaryotic microalgae in fluctuating light conditions, induced by
vertical mixing. PhD thesis, Catholic University of Nijmegen,
The Netherlands, 50–58.
Flynn KJ, Fasham MJR, Hipkin CR. 1997. Modelling the
interactions between ammonium and nitrate uptake in marine
phytoplankton. Philosophical Transactions of the Royal Society
London B 352 : 1625–1645.
Flynn KJ, Flynn K. 1998. Release of nitrite by marine
dinoflagellates : development of a mathematical simulation.
Marine Biology 13 : 455–470.
Flynn KJ, Page S, Wood G, Hipkin CR. 1999. Variations in the
maximum transport rates for ammonium and nitrate in the
prymnesiophyte Emiliania huxleyi and the raphidophyte
Heterosigma carterae. Journal of Plankton Research 21 : 355–371.
Geider RJ. 1987. Light and temperature dependence of the
carbon to chlorophyll a ratio in microalgae and cyanobacteria :
implications for the physiology of growth of phytoplankton.
New Phytologist 106 : 1–34.
Geider RJ, MacIntyre HL, Kana TM. 1998. A dynamic
regulatory model of phytoplanktonic acclimation to light
nutrients and temperature. Limnology and Oceanography 43 :
679–694.
Geider RJ, Platt T. 1986. A mechanistic model of photoadaptation in microalgae. Marine Ecology Progress Series 30 :
85–92.
Haefner JW. 1996. Modeling biological systems. London, UK :
Chapman & Hall.
Hee Kim J, Nemson JA, Melis A. 1993. Photosystem II
reaction centre damage and repair in Dunaliella salina (green
alga). Plant Physiology 103 : 181–189.
Herzig R, Falkowski PG. 1989. Nitrogen limitation in Isochrysis
galbana (haptophyceae), I. Photosynthetic energy conversion
and growth efficiencies. Journal of Phycology 25 : 462–471.
Hind G, McCarty RE. 1973. The role of cation fluxes in
chloroplast activity. In : Giese AC, ed. Photophysiology. New
York, USA : Academic Press, 113–156.
Jassby D, Platt T. 1976. Mathematical formulation of the
relationship between photosynthesis and light for phytoplankton. Limnology and Oceanography 21 : 540–547.
Kamykowski D, Janowitz GS, Kirkpatrick GJ, Reed RE.
1996. A study of time-dependent primary productivity in a
natural upper-ocean mixed layer using a biophysical model.
Journal of Plankton Research 18 : 1295–1322.
Kana TM, Glibert PM. 1987. Effects of irradiances up to 2000
µE m−# s−" on marine Synechococcus WH7803-II, photosynthetic responses and mechanisms. Deep Sea Research 34 :
497–516.
Kolber Z, Zehr J, Falkowski P. 1988. Effects of growth
irradiance and nitrogen limitation on photosynthetic energy
conversion in photosystem II. Plant Physiology 88 : 923–929.
RESEARCH Photoinhibition model
Kromkamp J, Limbeek M. 1993. Effect of short-term variation
in irradiance on light harvesting and photosynthesis of the
marine diatom Skeletonema costatum : a laboratory study
simulating vertical mixing. Journal of General Microbiology
139 : 2277–2284.
Marra J. 1978a. Effect of short-term variations in light intensity
on photosynthesis of a marine phytoplankter : a laboratory
study. Marine Biology 46 : 191–202.
Marra J. 1978b. Phytoplankton photosynthetic response to
vertical movement in a mixed layer. Marine Biology 46 :
203–208.
Marra J. 1980. Vertical Mixing and primary production. In :
Falkowski PG, ed. Primary productivity in the sea. London,
UK : Plenum Press, 121–137.
Mayes SR, Cook KM, Self SJ, Zhang Z, Barber J. 1991.
Deletion of the gene encoding the photosystem II 33 kDa
protein from Synechocystis sp. PCC 6803 does not inactivate
water splitting but increases vulnerability to photoinhibition.
Biochimica et Biophysica Acta 1060 : 1–12.
Nanninga HJ, Tyrell T. 1996. Importance of light for the
formation of algal blooms by Emiliania huxleyi. Marine Ecology
Progress Series 136 : 195–203.
Ogren E. 1991. Prediction of photoinhibition of photosynthesis
from measurements of fluorescence quenching components.
Planta 184 : 538–544.
Ohad I, Kyle J, Arntzen CJ. 1984. Membrane protein damage
and repair : removal and replacement of inactivated 32kilodalton polypeptides in chloroplast membranes. Journal of
Cell Biology 99 : 481–485.
Oquist G, Chow WS, Anderson JM. 1992. Photoinhibition of
photosynthesis represents a mechanism for the long term
regulation of photosystem II. Planta 186 : 450–460.
Paasche E. 1968. Marine planktonic algae grown with light dark
cycles II. Ditylum brightwelli and Nitzschia turgidula. Physiologia Plantarum 21 : 66–77.
Paerl HW, Tucker J, Bland PT. 1983. Carotenoid enhancement
and its role in maintaining blue green algal (Microcystis
aeruginosa) surface blooms. Limnology and Oceanography 28 :
847–857.
Pahl-Wostl C, Imboden DM. 1990. DYPHORA-a dynamic
model for the rate of photosynthesis of algae. Journal of
Plankton Research 12 : 1207–1221.
Park Y, Chow WS, Anderson JM. 1995. Light inactivation of
functional photosystem II in leaves of peas grown in moderate
light depends on photon exposure. Plant 196 : 401–411.
Post AF, Dubinsky Z, Wyman K, Falkowski PG. 1984.
Kinetics of light-intensity adaptation in a marine planktonic
diatom. Marine Biology 83 : 231–238.
Prezelin BB, Matlick HA. 1980. Time-course of photoadaptation in the photosynthesis-irradiance relationship of a
359
dinoflagellate exhibiting photosynthetic periodicity. Marine
Biology 58 : 85–96.
Prezelin BB, Matlick HA. 1986. Photosystem II photoinhibition
and altered kinetics of photosynthesis during nutrient dependent high light photoadaptation in Gonyaulax polyedra.
Marine Biology 93 : 1–12.
Raven JA. 1989. Fight or flight : the economics of repair and
avoidance of photoinhibition of photosynthesis. Functional
Ecology 3 : 5–19.
Raven JA, Samuelsson G. 1986. Photoinhibition at low
quantum flux densities in a marine dinoflagellate (Amphidinium
carterae). Marine Biology 70 : 21–26.
Richardson K, Beardall J, Raven JA. 1983. Adaptation of
unicellular algae to irradiance : an analysis of strategies. New
Phytologist 93 : 157–191.
Rivkin RB. 1990. Photoadaptation in marine phytoplankton :
variations in ribulose 1,5-biphosphate activity. Marine Ecology
Progress Series 62 : 61–72.
Rmiki NE, Brunet C, Cabioch J, LemoineY. 1996. Xanthophyll cycle and photosynthetic adaptation to environment in
macro-and microalgae. Hydrobiologia. 326/327 : 407–413.
Sathyendranath S, Lazzara L, Prieur L. 1987. Variations in
the spectral values of specific absorption of phytoplankton.
Limnology and Oceanography 32 : 403–415.
Shipton CA, Barber J. 1992. Characterisation of photoinduced
breakdown of the D1-polypeptide in isolated reaction centres of
photosystem II. Biochimica et Biophysica Acta 1099 : 85–90.
Smith BM, Morrisey PJ, Guenther JE, Nemson JA, Harrison
MA, Allen JF, Melis A. 1990. Response of the photosynthetic
apparatus in Dunaliella salina (green algae) to irradiance stress.
Plant Physiology 93 : 1433–1440.
Sournia A. 1974. Circadian periodicities in natural populations of
marine phytoplankton. Advances in Marine Biology 12 :
325–389.
Steeman Nielsen E. 1962. Inactivation of the photochemical
mechanism in photosynthesis as a means to protect the cells
against too high light intensities. Physiologia Plantarum 15 :
161–171.
Sukenik A, Wyman KD, Bennett J, Falkowski PG. 1987. A
novel mechanism for regulating the excitation of photosystem
II in green alga. Nature 327 : 704–707.
Tyystjarvi E, Ali-Yrkko K, Kettunen R, Aro EM. 1992. Slow
degradation of the D1 protein is related to the susceptibility of
low light grown pumpkin plants to photoinhibition. Plant
Physiology 100 : 1310–1317.
Weis E, Berry JA. 1987. Quantum efficiency of photosystem II in
relation to ‘ energy’-dependent quenching of chlorophyll fluorescence. Biochimica et Biophysica Acta 894 : 198–208.
Yoder JA, Bishop SS. 1985. Effects of mixing induced irradiance
fluctuations on photosynthesis of natural assemblages of coastal
phytoplankton. Marine Biology 90 : 87–93.