A Mechanistic Model of PhotoinhibitionAuthor(s): Helen L. Marshall, Richard J. Geider, Kevin J. FlynnSource: New Phytologist, Vol. 145, No. 2 (Feb., 2000), pp. 347-359Published by: Blackwell Publishing on behalf of the New Phytologist TrustStable URL: http://www.jstor.org/stable/2588959 .Accessed: 02/03/2011 14:31

Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unlessyou have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and youmay use content in the JSTOR archive only for your personal, non-commercial use.

Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at .http://www.jstor.org/action/showPublisher?publisherCode=black. .

Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printedpage of such transmission.

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact support@jstor.org.

Blackwell Publishing and New Phytologist Trust are collaborating with JSTOR to digitize, preserve and extendaccess to New Phytologist.

http://www.jstor.org

RESEARCH New Phytol. (2000), 145, 347-359

A mechanistic model of photoinhibition

HELEN L. MARSHALL 2*, RICHARD J. GEIDER 2 AND KEVIN J. FLYNN1

'Swansea Algal Plankton Research Unit, School of Biological Sciences, University of Wales-Swansea, Singleton Park, Swansea SA2 8PP, UK 2Marine Biological Association of the UK, Citadel Hill, Plymouth PL1 2PB, UK

Received 17 May 1999; accepted 20 October 1999

SUMMARY

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 Dl (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, Dl, model, reaction centre, quenching, photon flux density, quantum yield, absorption cross section.

INTRODUCTION

Recently, mathematical algal physiology models have begun to focus on mechanisms of photo- acclimation (Geider & Platt, 1986), nitrogen as- similation (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 ac- climate 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

capacity of the dark reactions (CO2 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) ac, the initial slope of the PE curve, which represents the light harvesting efficiency of the cell (g C g-1 Chl a (jimol photon m-2)-l)

(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 har- vesting ability of the cell (g C g-1 C d-1).

*Author for correspondence (fax +44 (0) 1792 295447; e-mail bdmarsha(swansea.ac.uk).

348 RESEARCH H. L. Marshall et al.

Table 1. The main features of photoinhibition

Event Reference

1 Damage to Dl in PSII reaction centres is a linear function of Adir et al. (1990); Hee Kim et al. (1993) photon dose

2 Dl proteins are continuously turned over Adir et al. (1990) 3 The quantum efficiency of PSII is decreased by damaged Dl Oquist et al. (1992) 4 Non-photochemical quenching decreases the PSII specific effective Smith et al. (1990); Oquist et al. (1992);

absorption cross section Falkowski & Raven (1997) 5 Damaged Dl are stabilised in the thylakoid as 160-kDa Baroli & MVielis (1996)

heterodimers, which perform a structural role 6 Excision of the 160-kDa heterodimers is the rate-limiting step in Baroli & Melis (1996)

repair

7 Damaged reaction centres provide protection from further Demmig & Bjorkman (1987) photodamage via non-photochemical quenching

8 Carotenoid/xanthophyll pigments provide non-photochemical Demmig & Bjorkman (1987) quenching, restricting further damage

9 Extent of inhibition depends on previous light and nutrient history Belay & Fogg (1978) Prezelin & Matlick (1986)

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 photo- inhibition 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 D 1 protein of photosystem I I (PS I I) reaction centres (Adir et al., 1990; Falkowski et al., 1994). Photo- damage does not suddenly begin at a given irradiance but occurs whenever cells are illuminated (Adir et al., 1990). The Dl protein is bound to the photo- oxidant P680, and the primary electron acceptor pheophytin (Mayes et al., 1991), and as such, damage to Dl has a probability of occurring every time there is a charge separation between P680 and pheophytin (Baroli & Melis, 1996; Anderson et al., 1998). The extent of D 1 damage may however also be dependent upon the presence or absence of oxygen (termed acceptor side photoinhibition), with Dl 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 Dl damage increases (Adir et al., 1990).

Dl is a 32-kDa protein, and is situated alongside a related 34-kDa form called D2. Damaged (i.e.

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 Dl 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 Dl 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 Dl 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 D 1, then moves back to PSII whereupon the 160-kDa heterodimer is excised, and the functional Dl inserted. De novo synthesis of Dl may be related to irradiance (Raven, 1989), the causal relationship is, however, unclear and RCII migration might well be triggered by Dl damage itself and therefore not be directly related to photon dose.

Newly synthesized Dl cannot be inserted into the reaction centre until the damaged Dl has been excised, because of the finite size of a reaction centre. Excision has been proposed to be the rate-limiting

RESEARCH Photoinhibition model 349

step in the repair cycle (Baroli & Melis, 1996). The presence of damaged Dl in the thylakoid provides a non-photochemical quenching defence against further photodamage (Oquist et al., 1992). Thus the Dl repair cycle may be used to moderate the total amount of damage sustained. This proposition is supported by the fact that the Dl 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 num- ber of factors. There may be two main forms of PSII in vivo, PSII,, and PSII, (Park et al., 1995). Park et al. (1995) proposed that 25 00 of PSII reaction centres exist as PSII,,(possessing a large light harvesting antenna), which are relatively more susceptible to damage than PSIIO. The ratio of these two forms was thought to be independent of total antenna size (and therefore of photoacclimative state). The loss of PSII,, 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 PSII, 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

PSII, 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 quench- ing 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

Dl damage (and therefore with PFD). Diadino- xanthin and diatoxanthin are the main components of the xanthophyll cycle in diatoms and prymnesio- phytes, however other algal groups posses different P-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 0 (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 ab- sorption cross section acts alongside Dl damage to decrease the initial slope (ac) of the PE curve (as ac is the product of the Chl a specific optical absorption cross section (a*), and the maximum quantum yield (4) m)).

A mechanistic simulation of photoinhibition is presented here, which takes into account the physio- logical 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.

MODEL DEVELOPMENT

The Dl 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 ac because of Dl 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 photo- synthesis 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 oc 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 Units

a* Chl a specific optical absorption cross section m2 g-1 Chl a ac Chl a specific initial slope of the PE curve m2 g 1 Chl a C1 ,tmol photon- B Slope constant for the dependence of non-photochemical d-1

quenching on 4 yield C Scaling factor enabling Qe to return a value between 1-0 Dimensionless Chlq Chlorophyll quota g Chl a g-1 C Chl a Level of Chl a g Chl a L` Dl Level of functioning Dl relative to the maximum level of Dimensionless

functioning D1 DD1 Level of damaged D1 present in the thylakoid relative to the Dimensionless

maximum level of damaged Dl dChl Chlorophyll a synthesis rate h-1 Ds Correction term for differential susceptibility to d-1

photodamage between species E Incident scalar irradiance ,tmol photons m-2 s-1

F Slope constant for the dependency of 4 yield on the relative Dimensionless level of active D1

Gd Gross D1 damage rate Dl D1-1 photons-1 m2 h-1 Kq Value of Q enabling half max. cell growth g N g-1 C Lh Light history (i.e. photon dose of the previous hour) Photons m2 h-1 N-status Calculation of N-status (returns value between 1-0) Dimensionless Pn Value of Rn after changing the value of Ra to Pa Units appropriate for parameter under

test PS Carbon specific rate of photosynthesis g C g-1 C d-1

Pmax Maximum C-specific photosynthetic rate g C g-1 C d-1 Pa Altered value of Ra Units appropriate for parameter under

test Q Cell N: C quota g N g-1 C QO Minimum cell N: C quota g N g-1 C Qe Antenna based non-photochemical quenching h-1 Rep Repair rate of damaged Dl in the thylakoid d-1 RChl Chl a degradation rate constant related to temperature d-1 Ra Normal parameter value Units appropriate for parameter under

test Rn Value of a chosen model parameter given the value of Ra Units appropriate for parameter under

test S Sensitivity index Dimensionless Ucoeff Normalizing factor giving C: N status as a value between Dimensionless

1-0

Vcn C-specific nitrogen uptake rate g N g-1 C d-1 X Scaling factor for conversion of photon dose into damage Dimensionless

rate Y Constant for the relationship between damaged Dl and the Dimensionless

repair rate Z Constant for the relationship between damaged Dl and the Dimensionless

repair rate

pChl Chl a synthesis regulation term Dimensionless 4) yield Quantum yield of photosynthesis g C g-1 C photon-1 4) m Maximum quantum yield g C g 1 C photon1

RESEARCH Photoinhibition model 351

a* ~~~~~amage a* Qe

Active Damaged a yield Dl Dl

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 + m

The level of active Dl affects the photon harvesting ability of PSII (ac), such that ac decreases alongside active Dl (Park et al., 1995). This decrease in ac is due to the closure of reaction centres, which leads to a decrease in the value of + yield (Park et al., 1995). A loss of up to 25 %0 of active DI proteins has been found not to decrease + 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 00 of active Dl may be lost without a decrease in + yield, after this threshold + yield decreases linearly with further decreases in DI (Park et al., 1995). Therefore + yield was modelled as a threshold process using Boolean logic (Eqn 3) such that it remains at the maximum value (+ m) until the relative level of active Dl as a proportion of total Dl reaches 0.75; + 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 + 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-photo- chemical 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

Table 3. Values for constants and parameter initialization

Constant/ initialization value Value Units

a* 0.00025 m2 g91 Chl a-1 B 8 Dimensionless Chlq 0.005 g Chl a g-1 C C 1 Dimensionless Dl 1 Relative DD1 0 Relative Ds 3.5 d-1 F 0.167 Dimensionless QO 0.0588 g N g-' C Q 0.17 g N g-1 C Ucoeff 0.5587 Dimensionless Vcn 0.04 g N g-1 C d-1 X 2 x 10-25 Dimensionless Y 1.163 Dimensionless Z 0.552 Dimensionless 4 m 0.125 g C g-1 C photon-1

differential susceptibility of different species to photodamage.

Dl damage

The rate of Dl 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 Dl 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, in- creasing 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 Dl, such that the rate constant for damage (the (X Lh) term in Eqn 5) is decreased as relative active Dl decreases, simulating the quench- ing provided by damaged DI. The protective effect of Qe (Eqn 4) is achieved by subtracting Qe from the damage rate (Eqn 5).

Dl repair

DI 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

xt c E * Chl Photosynthetic rate (g C g-1 C s-1), regulated by the 1 S=Plax tanh p qJ physiological status and irradiance (E). From Flynn

niax & Flynn (1998).

dCl p l ) Rate of Chl a synthesis (d-1). From Geider et al. 2 dha_(CVc-RChl'-Chl a (1998). dt - c9 3 Xyield = (F D1 Chlq fm) (F*D1)+(F D1 > m) m Regulation of Xyield by the level of functioning Dl in

the thylakoids. 4 Qe = B yield+C Antenna based non-photochemical quenching (h-1). 5 Gd = (X Lh) Dl Ds- Qe Gross intrinsic damage rate of active Dl proteins (Dl

Dl-1 h-1).

Y DD1 Rate of repair of damaged Dl within the thylakoids 6 Rep = N-status (Dl Dl-1 h-1). Z?DD1

(Q - QO)/(Q - Q.o+ Kq) Normalized nitrogen status, returning a value between 7 N-status - Ucoeff 1-0, where 1 is nitrogen replete. From Flynn et al.

Ucoeff ~~~~~~~~(1 999).

d Change in the level of active Dl in response to the Dl 8 D 1 = Dl * (Rep-Gd) damage and repair cycle.

dt

d Change in the level of damaged Dl in response to the 9 DD1 = DD1 (Gd-Rep) Dl damage and repair cycle.

dt 10 cx = a (1 - Qe) yield Regulation term for the initial slope of the PE curve

(m2 g-1 Chl a g-1 C ,umol photons-1).

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 Dl with and without repair (using inhibitors to block protein synthesis). As repair is triggered by (or in the same way as) Dl damage (Adir et al., 1990), repair was modelled as a function of the relative amount of damaged Dl (DD1 in Eqn 9).

Repair cannot be a linear response to the level of damaged Dl, 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 photo- damage at 1000 PFD, and so the maximum rate of repair is equal to the rate of Dl 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 Dl 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 Dl and DD1 are thus given as functions of repair and damage (Eqns 8, 9).

Formulation of ox

In Eqn 10, co is the product of the chlorophyll specific absorption cross-section (a*), and Q 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 (1 -Qe), 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.

RESULTS AND DISCUSSION

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 Dl were investigated (see Table 5 for response indices and index calculation). Sensitivity index values of 0 indicate no change in the level of active Dl 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.

DI damage and repair rates

Direct observations of Dl 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 fluor- escence is stoichiometrically related to the level of active Dl in PSII (Ogren, 1991; Falkowski & Raven, 1997), fluorescence data are used here as well as data on the level of active Dl, 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 Dl with increasing photon dose according to the exper- imental 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

0.8 -

'0.6- 0

a- 04- '

0.2 - 0

_ *

0.0 -

0 1 2 Photon dose (mol photons m2 h-1)

Fig. 2. Relative amount of functioning Dl present with increasing photon dose (non-steady state). Solid line shows model predictions (correction factor, Ds = 0.6), circular data points show experimental results redrawn from Park et al. (1995).

used to assess the efficiency of PS II, alongside model predictions for the change in active Dl (Ds = 1.2). As shown by Figs 2 and 3, model predictions of active Dl compare well with experimental results measuring both active Dl itself and Fv/Fm; how- ever, Fv/Fm must be measured after a period of dark relaxation to remove the rapidly relaxing com- ponents which are related to the functioning of Qe

The model can also simulate experimentally determined rates of Dl 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 Dl (Ds 0.65).

The only parameter which must be adjusted to simulate Dl damage and repair in different photo-

Table 5. Sensitivity analysis, showing the response of steady state levels of Dl and Qe to changes in constants affecting the DI damage and repair rates

Response index (S) Constant (normal value) Test value Active Dl Qe

Ds (1.5) 2.5 0.367 1.466 3.5 0.205 1.522 4.5 0.134 1.467

B (8) 7 1.189 1.315 9 0.853 0.763

Y (1.163) 0.581 3.901 na 1.744 0.623 na

Z (0.552) 0.276 -0.168 na 0.828 0.117 na

The index was obtained through model simulations of steady state growth, where C:N = 6 and PFD = 1000 [tmol m2 s-1 Unless stated otherwise Ds = 3.5. The analyses were performed using a single parameter sensitivity index from Haefner (1996), where S = (Ra-Rn/Rn)/(P-Pn/Pn).

354 RESEARCH H. L. Marshall et al.

1.2 1.2

1.0 1.0

E

0.4 - - 0.4 0

0O.6 --0.6

> -z U 0.2 - - 0.2

0.0 - 0.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Time (d)

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 Dl (continuous line) where the model was set up using the same conditions as in the experimental method (correction factor, Ds = 1.2).

35 30

30- 25

25- - 20

E20- E ~~~~~~~~~~~~~+

X 15 a U-15-

- 10 Q 10-

O- -

0- 0 i* I II I

0 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 Dl (correction factor, Ds = 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-photochemnical quenching. Further research into this area is re- quired, but the model's behaviour suggests that Dl damage and repair rates (per photon received by D1) might be universal, although the number of photons received by Dl 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

1.0-

0 0

0.8-

0.6-

0.4-

0.2-

0.0-

0 500 1000 1500 2000 2500 3000 3500 PFD (tmol m-2 s-1)

Fig. 5. Experimental results redrawn from Demmig- Adams et cal. (1989), showing the increase in antenna based non-photosynthetic quenching (Qe) with increasing pho- ton flux density (PFD) (solid circles), and model pre- dictions (solid line) (correction factor, Ds = 5).

up of protons (Bjorkman & Demmig-Adams, 1995). The model uses + yield to indicate the balance between these two reactions. A comparison of model output (Ds = 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 a 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 Dl 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 = 2000 ,umol m-2 S-1)

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 Dl1 is increased leading to a decrease in 4 yield (Prezelin & Matlick, 1986; Kolber et al., 1988; Herzig & Falkowski, 1989). During N-limitation, Isochrysis galbana shows a decrease in the number of open PSIJI reaction centres, accompanied by a decrease in 4 yield and

RESEARCH Photoinhibition model 355

0.8

0.7-

r 0.6-

O 0.5-

en 0.4- a)................................................................. .

.........

0.2- 0~ ? 0.2 - -- - - -

0.1

0.0

0 500 1000 1500 2000 PFD (tmol m-2 s-1)

Fig. 6. Model output for a hypothetical species (correction factor, Ds = 5), showing instantaneous rates of photo- synthesis with varying N-status. C: N = 6 (solid line), C: N = 9 (dotted line) and C: N = 13 (dashed line).

P max (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 (cyPSII) are species specific, but generally decrease with increasing PFD; however, some species (i.e. Thalassiosira weisflogii) may show no change in cyPSII at high PFDs (Kolber et al., 1988). N-limitation has been shown to increase cyPS11 (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 = 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 N- stressed cells (C:N = 13) show greater amounts of photoinhibition, and show photoinhibition at lower PFDs than N-replete (C: N = 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 P1ax (Prax 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.

1.0 2000

C-).

C>0.8 - -10 1500 L

0.3 0.4 0.N. .

E -1000 -

> ~~~~~~~~~~~~E co 0Q4 - 0

0.2-

0.3 0.4 0.5 0.6 0.7 Time (d)

Fig. 7. Model output showing changes in the relative photosynthetic rate (PS/Pniax, solid line) during a sinus- oidal light regime (dotted line). Correction factor, Ds = 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 sub- saturating 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 photo- synthesis 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 Dl 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

356 RESEARCH H. L. Marshall et al.

1.0

0.8- ______

400 u 0.6- \

04. ..

0.4-

0

cL 0.2 -

0.0 1 i I I I I I I

0 500 1000 1500 2000 2500 3000 PFD ([tmol m-2 s-1)

Fig. 8. Model output showing the time dependence of the photosynthetic rate (correction factor, Ds = 10) during N- replete growth. The lines represent cells acclimated to a sinusoidal light regime (1 2 h: 12 h, light: dark) with a maximum photon flux density (PFD) of 2000 [tmol m2 s sampled at the beginning of the photoperiod. Instan- taneous 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 measure- ments 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 Dl 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 photo- synthetic production at a givJen PFD (Marra, 1 978a). Fig. 8 shows model PE curves for incubations of different length, and the time dependency of the photosynthetic rate can be clearly seen, supporting

the conclusions from experimental work of Marra (1978a), and showing that a given measurement of photosynthetic production may not be independent of previous measurements.

Light fluctuations

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 associ- ated 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 ac- climate to different extents during fluctuating ir- radiance (Flameling & Kromkamp, 1997). The response is also highly dependent upon the frequency of the fluctuations (Flameling, 1998). Integrated daily photosynthetic production may be increased (Flamneling 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 Dl 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 fluctu- ating light may involve decreases in cell size, Chl a per cell and PSU size, and an increase inl PSU number (Flameling & Kromkamp, 1997). The photo-

RESEARCH Photoinhibition model 357

1000 3.0

800--25

C4~~~~~~~~~~~~~~~~~~~~~~~~~~~- 600 -) E

0.31.5 0. E/ ~-400 -~ LL ~~~~~~~~~~~~~~~1.0

200 -

0 0j

0.3 0.4 0.5 0.6 0.7 Time (d)

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 = 5).

inhibition model was configured to simulate fluctu- ating 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 fluctu- ating regime (0.634 mg-1 C g-1 C photon-1) than in the sinusoidal regime (0.485 mg-1 C g-1 C photon-1), 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 photo- synthesis. 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 photo- synthetic 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 oceano- graphic 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 0 of the surface illumination. If peak surface irradiance is taken to be c. 2000 [tmol m-2 s-1 PFD, the depth at which blooms form should receive a peak PFD around 1000 [tmol m-2 s-1 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 [tmol m-2 s-1 PFD (Nanninga & Tyrell, 1996), and so differential susceptibility to photo- inhibition (combined with aspects of nutrient acquisition), might explain the occurrence of species- specific 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 photo- acclimation (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 Dl measurements to clarify the nature of the time- dependent 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 xan- thophyll 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.

ACKNOWLEDGEMENTS

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.

REFERENCES

Adir N, Shochat S, Ohad I. 1990. Light dependent Dl 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 Dl protein degradation in peas acclimated to different growth irradiances. Plant Physiology 103: 835-843.

Barber, J. 1995. Molecular-basis of the vulnerability of photo- system 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 (Bacil- lariophyceae) 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 0, Demmig-Adams B. 1995. Regulation of photo- synthetic light energy capture conversion and dissipation in leaves of higher plants. In: Schulze ED, Caldwell MM, eds. Ecophysiology of photosynthesis. Berlin, Germany: Springer- Verlag, 17-47.

Claustre H, Gostan J. 1987. Adaptation of biochemical com- position and cell size to irradiance in 2 microalgae - possible ecological implications. Marine Ecology Progress Series 40: 167-174.

Critchley C. 1994. Dl protein turnover: response to photo- damage 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 photo- adaptation 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 02 evolution, photosynthetic capacity, and carotenoid composition during the midday depression of net CO2 uptake in Arbutus unedo growing in Portugal. Planta 177: 377-387.

Demmig B, Bjorkman 0. 1987. Comparison of the effect of excessive light on chlorophyll fluorescence (77K) and photon yield of 02 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 Scene- desmus protuberans (Chlorophyceae) to fluctuating PPFD simu- lating vertical mixing. Journal of Plankton Research 19: 1011-1024.

Flameling IA, Wyman K, Falkowski PG. 1998. Growth and photosynthesis of Thalassiosira weisfioggi 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.JYournal 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, Maclntyre 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 photo- adaptation 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 phyto- plankton. 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 uE m-2 s-1 on marine Synechococcus WH7803- II, photo-

synthetic responses and mechanisms. Deep Sea Research 34: 497-5 16.

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 359

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 Erniliania 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 32- kilodalton 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. Ditylutm brightwelli and Nitzschia turgidula. Physio- logia 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. Jfournal 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 photo- adaptation in the photosynthesis-irradiance relationship of a

dinoflagellate exhibiting photosynthetic periodicity. Marine Biology 58: 85-96.

Prezelin BB, Matlick HA. 1986. Photosystem II photoinhibition and altered kinetics of photosynthesis during nutrient de- pendent 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 (Anmphidiniurn 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. Xan- thophyll 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. Limnnology 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. Biochinmica 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 MVIarine 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 Plantaruim 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 Dl 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 fluor- escence. 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.