J. theor. Biol. (2002) 214, 519}527doi:10.1006/jtbi.2001.2468, available online at http://www.idealibrary.com on

A Mechanistic Model of Algal Photoinhibition Induced byPhotodamage to Photosystem-II

BO-PING HAN*-?

*Institute of Oceanography, Chinese Academy of Sciences, Qingdao 266071, People1s Republic of Chinaand -Institute of Hydrobiology, Jinan ;niversity, Guangzhou 510632, People1s Republic of China

(Received on 8 May 2001, Accepted in revised form on 3 October 2001)

Photoinhibition is a central problem for the understanding of plasticity in photosynthesis vs.irradiance response. It e!ectively reduces the photosynthetic rate. In this contribution, wepresent a mechanistic model of algal photoinhibition induced by photodamage to photo-system-II. Photosystem-IIs (PSIIs) are assumed to exist in three states: open, closed andinhibited. Photosynthesis is closely associated with the transitions between the three states.The present model is de"ned by four parameters: e!ective cross section of PSII, number ofPSIIs, turnover time of electron transfer chains and the ratio of rate constant of damage to thatof repair of D1 proteins in PSIIs. It gives a photosynthetic response curve of phytoplankton toirradiance (PI-curve).Without photoinhibition, the PI-curve is in hyperbola with the "rst threeparameters. The PI-curve with photoinhibition can be simpli"ed to the same form as thehyperbola by replacing either the number of PSIIs with the number of functional PSIIs or theturnover time of electron transfer chains with the average turnover time.

� 2002 Elsevier Science Ltd

Introduction

Quantitative representation of photosynthesis}irradiance response is at the base of estimationphotosynthetic production of waterbody on dif-ferent scales such as water column, regional andglobal oceans (Berger et al., 1989; Falkowski,1994; Kirk, 1994). A number of models have beendeveloped to describe photosynthetic response ofphytoplankton to irradiance (Smith, 1937; Steele,1962; Vollenweider, 1965; Platt & Jassby, 1976;Bannister, 1979; Megard et al., 1984; Eiler& Peeters, 1988; Sakshaug et al., 1989; Cullen,1990; Pahl-Wostl, 1992; Geider & Macintyre,1996). Among the existing models, none of them

? Institute of Hydrobiology, Jinan University, Guangz-hou 510632, People's Republic of China. E-mails: tbphan@ms.qdio.ac.cn, tbphan@jnu.edu.cn

0022}5193/02/040519#09 $35.00/0

can "t all the observation data or all the experi-mented organisms (Falkowski & Ravan, 1997).This has been recognized and attributed to plas-ticity in photosynthetic response of phytoplank-ton to irradiance. The plasticity mainly occurswhen phytoplankton are exposed to highirradiance or grow at low irradiance and it canbe modi"ed by other factors such as nutrients(Herzig & Falkowski, 1989). Therefore, knowledgeof photoinhibition is critical for understandingthe photosynthetic response of phytoplankton toirradiance.Photoinhibition is a phenomenon of decrease

in photosynthesis exhibited by plants, when theyare exposed to high irradiance. The decrease inphotosynthetic rate under high irradiance alsomay result from photoxidation and other causes.But photoinhibition is usually used to des-cribe the reduction of photosynthetic capacity,

� 2002 Elsevier Science Ltd

520 B.-P. HAN

independent of gross change in pigment concen-tration, induced by exposure to high irradiance(Powles, 1984; Long et al., 1994; Tyystjarvi &Aro, 1996). The photoinhibitory reduction inphotosynthetic rate may be a!ected by twomain processes: photodamage to and recovery ofphotosystem-IIs (PSIIs) and avoidance of over-excitation. An exhaustive review of photoinhibi-tion in phytoplankton and its signi"cance foraquatic production can be found in Harris (1978)and Long et al. (1994). In the last two decades, theunderstanding of photoinhibition mechanismsinduced by photodamage to PSIIs has beenlargely improved due to the application of mo-lecular biology (Ohad et al., 1990; Melis, 1991;Barber & Anderson, 1992; Sinclair et al., 1996).It is well known that PSII is the primary dam-

age target during photoinhibition of oxygenicphotosynthesis (Kok, 1956; Powles, 1984; Kyle,1987; Prasil et al., 1992). According to recentviews visible light can inactivate PSIIs by twodi!erent mechanisms, which are called acceptorside and donor side-induced photoinhibition.Although the two mechanisms are di!erent inprocess, a common feature is the degradation ofD1 protein that has been widely investigated andcon"rmed (Ohad et al., 1990; Styring et al., 1990;Nedbal et al., 1990; Telfer & Barber, 1994; Ander-son et al., 1997; Neidhardt et al., 1998). Based onthese molecular discoveries, a general mechanismof photoinhibition can be summarized as follows:a high irradiance causes a marked increase in theturnover rate of D1 protein, which is linked tothe requirement to repair PSII after it has beendamaged by photoinhibitory irradiation. Thephotoinhibition is controlled by balance betweendamage to and recovery of D1 protein (Tyystjarvi& Aro, 1996; Baroli & Melis, 1996; Andersonet al., 1997).Quantitative representation of photoinhibition

has received increasing attention. A number ofmodels have been developed to represent andevaluate the e!ect of photoinhibition on photo-synthesis (Pahl-Wostl & Imboden, 1990; Eilers& Peeters, 1993; Durate, 1995; Durate & Ferreia,1997; Zonneveld, 1998; Han et al., 2000, Marshallet al., 2000). Kok (1956) supposed that photosyn-thetic rate is proportional to the concentration ofa light-sensitive component that now is recog-nized to be PSII or reaction center protein. He

built a dynamic model of the concentration ofthe light-sensitive component. This early ideawas developed to express the change in photo-synthetic rate under UV-B treatment by Neale &Richerson (1987). Platt et al. (1980) empiricallyintroduced an inhibition parameter into a lightsaturated curve when irradiance is over a criticalvalue, but the biological mechanism behind thephotoinhibition parameter is lacking. The modelby Fasham&Platt (1983) was based on physiolo-gical processes associated with electron #owthrough PSII, the photoinhibition is incorpor-ated by expressing rate constant, at which anelectron donor is oxidized, as an exponentialfunction with a negative exponent. Pahl-Wostl& Imboden (1990) introduced an empiricaldynamic function of photoinhibition into anempirical static model. The two models byMegards et al. (1984) and Eiler & Peeters (1988)were established on transitions between threestates: open, closed and inhibited. Since the rateconstants for transitions were not de"ned in de-tail, the two models were simpli"ed bycompounding the rate constants into a fewparameters, and they have a common form:P(I)"I/(aI�#bI#C). When the inhibitedstate is ignored, the model is reduced to a lightsaturation curve. Although the models sharea common form, their descriptions of the recov-ery path of inhibited state are di!erent. In Mega-rd et al. (1984), one inhibited trap transists intoone closed trap before it becomes an open one.Whilst in Eiler & Peeters (1988), the inhibitedtrap is assumed to transit directly into an openone after repairing. Hence, the compoundparameters by the two models have di!erentmeanings.Recently, several models were developed to

investigate the e!ect of photoinhibition onphotosynthesis by incorporating the physiolo-gical and molecular mechanism underlyingphotoinhibition (Zonneveld, 1998; Han et al.,2000; Marshall et al., 2000). Zonneveld (1998)"rst reduced the three states of photosyntheticunits (PSUs) into two states (i.e. open and closed)and obtained a light saturated curve that hadturnover time as a parameter, and expressed theturnover time of electron transfer chains asa function of D1 protein concentration. In Mar-shall et al. (2000), photoinhibition is described as

PHOTOINHIBITION MODEL 521

a time-dependent decrease in the initial slope ofa PI-curve, related to D1 damage and non-photochemical quenching. In our previous study(Han et al., 2000), the average turnover time ofelectron transfer chains is de"ned as a function ofrelative concentration of D1 proteins. Photoin-hibition processes due to D1 protein degradationwere incorporated into a function of photosyn-thetic rate that was initiated by Dubinsky et al.(1986) and developed by Sakshaug et al. (1989).Although these models adopt the molecular pro-cesses of photoinhibition and can mathematicallydemonstrate the reduction in the photosyntheticrate, they are not su$cient to interpret photoin-hibition because of the utilization of the empiricalmodels of photosynthesis. For a single PSII, itloses activity when its reaction center protein D1is damaged, while the turnover time of an indi-vidual electron transfer chain does not change.As photoinhibition stems from the decrease infunctional PSIIs, the decrease in turnover time ofelectron transfer chains addresses photoinhibi-tion only on average over all the PSIIs. In thiscontribution, we follow the assumption oftransitions between the three states of photosyn-thetic machine byMegard et al. (1984), and devel-op a mechanistic model of algal photoinhibitioninduced by photodamage to PSIIs. The modelcan be used to present mechanisms underlyingphotoinhibition and evaluate the e!ect of photo-inhibition on photosynthetic rate.

The Model

Photosynthetic unit (PSU) is a basic functionalelement in the study of plasticity in photosyn-thesis vs. irradiance response. It is referred to asan ensemble of chlorophylls that interact to pro-duce one molecule of O

�and comprises elemen-

tary components for photosynthesis such asPSIIs, PSIs and electron transfer chains (Prezlin,1981; Mauzerall & Greenbaum, 1989). In a PSU,Z-scheme of photosynthesis works step by stepfrom PSII to PSI, but all the absorbed energy bya PSU is not transported to the PSII, for PSI hasits own light absorption. After being hit byphotons, the PSII transits from an open state toa closed one. Accordingly, the PSU becomesclosed. For simplicity, here, we assume thata PSU contains one PSII, corresponding to an

electron transport chain (Sukenik et al., 1987).The minimal time required for an electron totransfer from water on the donor side of PSII toterminal electron acceptors is called turnovertime of an electron transfer chain, noted as �. It isassumed to be constant and determines the po-tential photosynthetic rate. PSIIs exist in threephysiological states: open (or reactive), closed (oractivated) or inhibited. Photosynthetic processesare closely associated with transitions betweenthe three states. Figure 1(a) demonstratestransition rates between the three states. Theprobabilities of PSIIs at the three states are notedas A, B and C, respectively. After absorbingphotons, PSIIs transfer from an open state to aclosed state at a rate that is proportional to thee!ective light absorption (�

����I). Excessive ab-

sorption leads to photoinhibition at a rate ofk������

I, then recovering at a rate of k�(s��).

Here, I is irradiance in Einsteinm�� s��, �����

isthe e!ective absorption cross-section of PSII inm� quantum��. The e!ective cross-section is re-lated to the optical absorption cross-section ofPSU (�

���, in m� mol O��

�) and the maximal

quantum yield for oxygenic evolution (����, in

molO�quanta��) as �

���"�

����/�

���(Dubinsky,

1992). The dynamics of PSIIs at the three statescan be described by the following di!erentialequations:

dAdt

"!I�����

A#

B�, (1a)

dBdt

"I�����

A!

B�#k

�C!k

������

IB, (1b)

dCdt

"!k�C#k

������

IB, (1c)

where A#B#C"1. As steady state, the solu-tion is given as

A"

11#�

����I�#(k

�/k

�) (�

����I)��

, (2a)

B"

�����

I�1#�

����I�#(k

�/k

�)(�

����I)��

, (2b)

C"

(k�/k

�) (�

����I)��

1#�����

I�#(k�/k

�) (�

����I)��

. (2c)

FIG. 1. (a) Transitions between three states of PSIIs: open,A; closed, B and inhibited, C. � is the minimal turnover timeof electron transfer chains, �

����the e!ective cross-section of

a PSII, k�the damage constant for PSIIs, k

�the repairing

rate of damaged PSIIs. (b) PI-curve without photoinhibition(solid line) and the Pl-curve with photoinhibition (dottedline), where K"k

�/k

�, P

�"N/�, I

"1/(�

�����), PM

�"N/

(�#2�K�), IM"1/(�

����(�#2�K�)), IM

�"1/(�

�����K�).

522 B.-P. HAN

The quantum yield for oxygenic evolution is pro-portional to the probability of PSIIs at openstate, i.e �(I)"�

���A. We obtain photosynthetic

response to irradiance at steady state as follows:

P(I)"aI����

11#�

����I�#(k

�/k

�) (�

����I)��

,

(3)

where a is the speci"c absorption e$ciency ofchlorophyll-a in m�mg-chlorophyll-a��. Assum-ing N PSUs per mg-chlorophyll-a, i.e. a"N�

���,

we obtain a PI-curve at steady state as

P(I)"N�����

I1#�

����I�#K(�

����I)��

, (4)

where K is the ratio of k�/k

�in s��. As k

�and k

�are two parameters describing dynamics of reac-tion centers at inhibited state,K is the parametercharacterizing the dynamics of inhibited PSIIs.The performance of photoinhibition is dependenton the cross-section of PSII and the constant K.Without considering photoinhibition, i.e. K"0,eqn (4) gives a PI-curve in hyperbola

P(I)"N�����

I1#�

�����I. (5)

This curve has an initial slope of S�"N�

����and a maximal photosynthetic rate of P

�"N/�,

which have been widely recognized (Falkowski,1992; Sakshaug et al., 1997). Equation (5) can berearranged in the following form:

P(I)"P�

II#I

, (6)

where I"1/(��

����), corresponding to the irra-

diance at which the photosynthetic rate ishalf-maximum. Equation (6) has been used em-pirically and it was extensively discussed in Han(2001).

In6uence of Photoinhibition on PI-curve

From eqn (4), we can obtain four characteristicparameters of the PI-curve, i.e. PM

�2maximal

photosynthetic rate, IM�2optimal intensity,

S�*initial slope and I

*the half-saturation

irradiance, they are in the following forms:

PM�"

N

�#2�K�, IM

"

1

�����

(�#2�K�),

S�"N�

����, IM

�"

1

�����

�K�.

Here, PM�, I�

�and IM

decrease with K, there exists

no relationship between the initial slope and inhi-bition. Without consideration of inhibition, i.e.K"0, we have

P�"

N�, I

"

1�����

�, I

�"R.

PHOTOINHIBITION MODEL 523

Except the initial slope, the characteristic para-meters of photosynthetic response to irradianceare modi"ed by photoinhibition. The modi"ca-tion can be expressed as follows:

PM�

P�

"

1

1#2�K/�,

IMI

"

1

1#2�K/�.

Thus, the modi"cation of characteristic para-meters is dependent on K, which characterizesthe sensitivity of photosynthetic systems to thephotodamage by high irradiance, while the per-formance of photoinhibition is associated withturnover time of electron transport chain (�). Un-der a given K, phytoplankton with higher turn-over rate (1/�) have more sensitive performanceto photoinhibition. The e!ect of photoinhibitionon the photosynthetic response of phytoplanktonto irradiance is illustrated in Fig. 1(b).

Discussion

DYNAMICS OF D1 PROTEINS AND PHOTOINHIBITION

The primary target of photoinhibition is PSII,which is inhibited, physically damaged and laterrepaired. During photoinhibition, the rapid turn-over of D1 protein was discovered (see review byPrasil et al., 1992). In the reactions that coupledto degradation of the D1 protein, new copies ofD1 protein are synthesized and later inserted intoPSII complexes devoid of D1 protein. Activationof new PSII centers demands rebinding of thechlorophylls, pheophytins, quionones, the accep-tor side iron and donor side Mn ions. In aprevious contribution, Han et al. (2000) builta simple equation for dynamics of D1 proteinunder photoinhibition

d�dt

"!k������

I�#k�(1!�), (7)

where � is the relative concentration of D1 pro-tein. For an individual PSII, it loses activity whenits D1 protein is damaged. Thus, the damage andrepair of D1 protein exactly keep up with theinhibition and recovery of PSIIs. That is to saythat the two parameters: k

�and k

�in eqn (7) have

the same meanings as eqns (1)}(4). The two rateconstants can be measured directly or indirectly

in experimental condition (Baroli & Melis, 1996;Tyystjarvi & Aro, 1996).It is noteworthy that the relative D1 protein

was mistakenly de"ned in the previous model byHan et al. (2000). For a PSII, it transfers from anopen to a closed state after absorbing photons,excess absorption results in damage to D1 pro-tein. For an algal cell, the photoinhibition in-creases with transition of PSIIs from closed stateto inhibited PSIIs. Equation (7) describes therelative D1 protein dynamics in the closed andinhibited states. Therefore, � indicates the pro-portion of D1 proteins in closed PSIIs to the totalin closed and inhibited PSIIs, rather than thefunctional D1 protein concentration as de"nedearlier. The ratio: B/(B#C) de"nes the propor-tion of D1 proteins in closed PSIIs to the total inboth closed and inhibited states. By applyingeqns (2b) and (2c), the ratio of B/(B#C) canyield

�"

k�

k�#k

������

I. (8)

This result corresponds exactly to the solution ofeqn (7) at steady state.

TURNOVER TIME OF ELECTRON TRANSFER CHAINS,

NUMBER OF PSIIs AND PHOTOINHIBITION

Photosynthesis at subsaturating irradiance israte limited by light absorption and excitationenergy transfer to PSII reaction centers. At lightsaturation, photosynthesis is limited on the ac-ceptor side of PSII, generally by the capacity ofenzymatic processes in the Calvin cycle, i.e. 1/�(Sukenik et al., 1987). This down-stream limita-tion ultimately restricts electron turnoverthrough PSIIs. The light saturated rate of elec-tron transfer can be expressed as the product ofPSII number and turnover rate of electron trans-fer chains. Theoretically, the e!ect of photoin-hibition on photosynthesis should depend uponwhich step in the photosynthetic electron transferchain is rate limiting at a given irradiance. Initialrate limitation of the acceptor side of PSIIimplies that photoinhibition will not a!ectthe maximal photosynthetic rate until the num-ber of functional PSIIs evidently decrease. Dur-ing photosynthetic reactions, PSIIs exist in one ofthe three states: open, closed or inhibited. Both

524 B.-P. HAN

open and closed PSIIs are functional, while in-hibited PSIIs are damaged or unfunctional. Asdamaged PSIIs increase with irradiance, theaverage turnover rate over all electron transferchains reduces or the average turnover time in-creases. This can be demonstrated by rearrangingeqn (4) in the following from:

P (I)"N�����

I1#�

����I�*

, (9)

�*"�(1#K�����

I), (10)

where �* is the average turnover time of electrontransfer chains. In Han et al. (2000), the averageturnover time is related to the relative D1 proteinconcentration as �*"�/�. Equation (10) can beobtained by combining �*"�/�

and eqn (8).

As argued above, however, photoinhibitionvirtually results from a decrease in functionalPSIIs. It is best to represent photoinhibition witha decrease in functional PSIIs. We rewrite eqn (4)in the following form:

P(I)"N1#�

����I�

1#�����

I�#K(�����

I)�������

I1#�

����I�.

(11)

The "rst two terms on the right-hand side ofeqn (11) de"ne the total number of PSIIs at bothopen and closed states, i.e. the number of thefunctional PSIIs, we note is N*. Equation (11)can be simpli"ed as

P(I)"N*�����

I1#�

����I�, (12)

N*"N1#�

����I�

1#�����

I�#K(�����

I)� �. (13)

The functional PSIIs (N*) decrease with irra-diance.

INFLUENCE OF PHOTOADAPTATION ON

PHOTOINHIBITION PERFORMANCE

When phytoplankton grow in low irradiance,light becomes the factor limiting phytoplanktonphotosynthesis. Under such conditions of low-energy supply, algal cells regulate their photosyn-

thetic apparatus to maximize energy utilization.The most obvious regulation is an increase inthe cellular chlorophyll content. According to thesuggestion from Prezlin (1981), this increasemight consist in an increase in the amount ofchlorophyll per PSU (i.e. size of PSU), or anincrease in the number of PSU.Although photoinhibition and photoadapta-

tion are controlled by relatively independentmechanisms, the interaction between them hasbeen realized for a long time. The direct evidenceis that dark-adapted or low light acclimatedalgae usually show a higher initial slope ofPI-curve but a lower maximal photosyntheticrate, and show photoinhibition at low irradiance(Harris, 1978; Marra, 1978a, b). These observa-tions have not been covered yet by the publishedmodels, as pointed out by Vincent (1990), Ferris& Christian (1991) and Falkowski et al. (1994).However, the present model seems to enable us toinvestigate the relationship between photoadap-tation and photoinhibition. When phytoplank-ton adapt to low irradiance, the evident changesin physiological state are quantitatively related tothe number of PSIIs, the optimal and e!ectivecross-sections, e.g. N, �

���and �

����(Falkowski,

1981; Dubinsky et al., 1986). The increase in thenumber of PSIIs leads to the increase in theinitial slope (�

����N) and maximal photosynthetic

rate (P�"N/�). The increase in PSU size may

contribute to �����. However, an increase in

�����

consequently results in a stronger damage toD1 protein when exposed to high irradiance, asthe amount of photons absorbed by PSII is pro-portional to �

����. Thus, a reduction of photosyn-

thetic rate due to the increasing �����

can beexpected with photoinhibition. In eqn (10), theaverage turnover time of electron transfer chainsis a linear function of �

����. An increase in

�����

can enhance photosynthetic rate at low irra-diance but suspensicity to photoinhibition athigh irradiance. Therefore, a change in physiolo-gical parameter �

����appears to be able to pro-

vide a possible explanation of photoinhibition ofshade-grown phytoplankton. The two strategiesfor photoadaptation, an increase in the numberof photosynthetic units (N-strategies) and an in-crease in their sizes (�

����-strategy), have di!erent

e!ects of photoinhibition. The increase in thenumber of PSU enhances not only the initial

PHOTOINHIBITION MODEL 525

slope but also the maximal photosynthetic rate.The increase in the size of PSUs improves photo-synthetic e$ciency only at low irradiance. As thesynthesis of PSIIs is much more energy consum-ing than the synthesis of chlorophyll molecules,these two photoadaptation strategies are selectedby phytoplankton growing in di!erent lightenvironment. Phytoplankton in stable low lightregime trend to follow �

����-strategy, while in

unstable low light regime, phytoplankton arereadily exposed to high irradiance and preferN-strategy (Behrenfeld et al., 1998).

Concluding Remarks

To represent the photosynthetic response ofphytoplankton to irradiance at the physiologicallevel is not a new idea, it was suggested years ago(reviewed by Falkowski & Raven, 1997). Thethree physiological parameters in eqn (5) havebeen measured in the laboratory and naturalconditions by means of a pump-and-probe #u-orescence technique or a pump-during-probe fora single cell (Kolber & Falkowski, 1993; Olsonet al., 1996). Towards this objective, an empiricalPI-curve that associated with the three para-meters was suggested in exponential form asP (E)"P

�(1!e������� ) (Dubinsky et al., 1986).

This PI-curve was obtained by extending theaccumulative one-hit Poisson function for con-tinuous light. However, it is reasonable only froman empirical viewpoint.The present model is developed on the basis of

the existing models such as those by Megardet al. (1984), Dubinsky et al. (1986), Elier &Peeters (1988), Zonneveld (1998) and Han et al.(2000). It can produce photosynthetic rate com-parable to experimental data. It is strongly con-nected to a classical equation "rst proposed byHaldane (1930) for enzyme reactions that areinhibited by high concentration of substrate, andto Kok's (1956) representation of the dynamics oflight sensitive component. We found that thephotosynthetic response of phytoplankton to ir-radiance can be addressed in a simple model. Byuse of a few physiological parameters, the simplemodel provides biological mechanisms thatunderlie the existing empirical PI-curves such asthe one given in Steele (1962). By comparingeqns (9) and (12) to eqn (5), it can be suggested

that the PI-curve in hyperbola as eqn (5) isa basic mode of photosynthetic response ofphytoplankton to irradiance. It reveals the sim-plicity behind photosynthetic processes of thephytoplankton. The e!ect of photoinhibition onthe photosynthetic rate can be explicitly evalu-ated through the average turnover time of elec-tron transfer chains and the number of functionalPSIIs. From molecular biology viewpoint,photoinhibition is the result of two simultaneousprocesses: light-induced damage to and concur-rent recovery of D1 protein. The parameters k

�and k

�in the present model correspond to the

rate constants for damage and repair of D1proteins, respectively. Hence, the present modelprovides a link between ecology and molecularbiology on phytoplankton photosynthesis. Itshould be pointed out that the present model isgiven on the assumption that a PSU has onePSII. As a photosynthetic unit is de"ned as chlo-rophyll molecules involved in an O

�molecule

during a #ash, it contains four PSIIs to simulta-neously split two water molecules. In this case,the e!ective cross-section of PSIIs is contributedby four PSIIs, and the four PSIIs at open stateare needed to cooperate for the evolution of anindividual O

�molecule. This does not a!ect the

PE-curve. It must be argued that in naturalconditions, variations in the model parameterscan be found. The variations characterizephytoplankton adaptation to di!erent lightregimes. It may be modi"ed by other environ-mental factors such as nutrients. Given that thedata on these parameters have been accumulat-ing in the large-scale biological}oceanographyobservations, the present model can be expectedto have a wide application.

I am grateful to M. Straskraba, I. Setlik and Y.Dandonneau for their encouragement and suggestion.I also thank one anonymous referee for his valuablecomments that improved largely my understanding ofphotoinhibition. Support from Chinese Academy ofSciences (No. 131, the 100-talent project), the NSFC(No. 39900022), the Yingdong He education founda-tion (No. 71020) and IRD of France is acknowledged.

REFERENCES

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