Deep-Sea Re~earch. Vol. 38. No. 4, pp. 415--4311. 19ql. 0198-0140/91 $3.011 -*- 0.fin Prmted ill Great Bntam. ~ lt~O[ Pergamon Prexs plc

Modeling of light-dependent algal photosynthesis and growth: experiments with the Barents Sea diatoms Thalassiosira

nordenskioeldii and Chaetoceros furcellatus

EGIL SAKSHAUG,* GEIR JOHNSEN,* KJERSTI ANDRESEN* a n d MARIA VERNETS"

(Received 12 March 1990; in revised form 6 September 1990; accepted 1 October 1990)

Abstract--The models by SAKSHAUG et al. (1989, Limnology and Oceanography. 34. 198-205) and WEBB et al.( 1974, Oecologia, 17, 281-291), for prediction of the gross growth rate of phytoplankton and short-term photosynthesis, respectively, have been modified on the basis of experiments with cultures of the centric diatoms Thalassiosira nordenskioeldii and Chaetocerosfurcellatus grown at 0.5°C at combinations of two irradiances (25 and 400~mol m -z s - t ) and two day-lengths (12 and 24 h). The models have one spectrum. *o. which represents chlorophyll a (Chin) specific absorption of photosynthetically usable light, and introduces a factor q which represents Chin per PSU. functionally defined. The models describe phytoplankton growth in terms of physiologically relevant coefficients.

A properly scaled fluorescence excitation spectrum (°F) represents a more appropriate estimate for °tl than the Chin-specific absorption spectrum °a~ judging from calculations of c!%,,~ (=t~/°o) . On the basis of °F. ~lJ,,,,~ is I).114 g-at C(mol photons)-i for gross growth and about 0.115-0.08 for short-term carbon uptake (unfiltered samples). Calculations based on *a~ yield values for 'l~m,,~ which on average are 44% lower.

P vs I (photosynthesis vs irradiance) parameters are relatively independent of day-length and highly dependent on growth irr:tdiance. The product of q [mg Chin (mol PSU) -I] and r (the minimum turnover time of the photosynthetic unit, h) increases 2-3-fold from high to low irradiance, thus p u (=Cl~m~x/qr) and I k (=l/qr°o) decreased. °F decreases from high to low irradiance. Carbon-specific dark respiration rates are <0.09 day- t.

Pigment ratios vary inversely with irradiance and day-length. The Chin: C ratio is particularly low under high, strong continuous light; Chic:Chin ratios are higher for shade- than for light- adapted cells, while the converse is true for the ratio of the sum of the photoprotective pigments diadinoxanthin and diatoxanthin to Chin. The fucoxanthin : Chin ratio is virtually independent of the light regime.

The two species are similar with respect to variations in growth rate (0.09--11.33 day- t ) and/~ (31-36 vs 49-1(X)l~mol m -z s- i at low and high irradiance, respectively). P~m and a a for growth as well as °F are systematically higher for C. furcellatus than for T. nordenskioeldii, while the product qr is lower. C. furcellatus is considerably more plastic than T. nordenskioeldii with respect to pigment composition.

I N T R O D U C T I O N

MATHEMATICAL m o d e l s o f algal p h o t o s y n t h e s i s a n d g r o w t h a r e i m p o r t a n t in t h e p r e d i c t i o n

of global- and regional-scale variations in marine primary productivity and are used in the

"Trondhjem Biological Station. The Museum, University of Trondheim, Bynesveien 46, N-7018 Trondheim, Norway.

* Polar Research Program, A-002, Scripps Institution of Oceanography, University of California at San Diego, La Jolla. CA 921193, U.S.A.

415

416 E. S~SHAt;G et at.

conversion of Chlorophyll a data obtained by remote sensing to primary production and algal growth. Marine photosynthesis has been modeled as a function of irradiance by numerous authors (see RrrnEx, 1956; RrrrlEa and YENTSCH, 1957; JASSa¥ and PLArr, 1976; PLArr et al., 1980; FALKOWSrJ, 1981; CULLEN, 1990 and references therein). P vs I (photosynthesis vs irradiance) formalism, which, strictly speaking, defines short-term gross photosynthesis, is inherent in some of the models.

In addition to P vs I models, there are steady-state models that describe light-dependent gross growth rate (BANNISTE~ and LAws 1980; KmFEX and MrrCHELL, 1983; GEnDeR et al., 1986; SAKSHAUG et al., 1989). The model by SAKSHAtJG et al. (1989) for nutrient-deficient Skeletonema costatum growth at different irradiances and day-lengths represents an extreme simplification since only the Chla:C ratio varies, while photoadaptive variations in the P vs I coefficients are neglected. These types of models require, however, knowledge of the Chla :C ratio which is notoriously difficult to measure in the field, On the other hand, they can be modified to predict daily adapted growth, in principle, by replacing the Chla 'C ratio with the Chla concentration (CULLEN, 1990).

In contrast to the study by SAKSHAU~ et al, (1989), we have studied nutrient-saturated cultures. Thalassiosira nordenskioeldii and Chaetoceros furcellatus were grown at combi- nations of two different irradiances and day-lengths with the purpose of (i) identifying thc key variables necessary to model growth from photosynthetic parameters, (ii) ascertaining the effect of photoadaptation to the predictive capability of the model, and (iii) testing the generality of the model of SAKSHAUG et al. (1989) to Arctic phytoplankton. Few investi- gations so far have dealt with the day-length dependent photosynthetic response of phytoplankton (Pcrr et al.. 1988; CARON et al., 1988). Measurements include carbon uptake (P vs I curves), growth and dark respiration rates, and the cellular composition. To study the variability in relevant physiological parameters in a convenient fashion, wc havc suggested a modification of the model by SAKSrlAUG et al. (1989). We have also evaluated the use of light absorption spectra vs scaled fluorescence spectra for calculation of harvested photosynthetically usable light.

The centric diatoms T. nordenskioeldii and C. furcellatus Bailey have northerly distributions and occur regularly in the Barents Sea, although usually without being predominant. T. nordenskioeldii may be regarded as an Arctic-boreal species, while C, furcellatus is a more obligately arctic species (HEIMDAL, 1974; Hasle, 1976).

MATERIALS AND METHODS

T. nordenskioeldii Cleve, clone PMTn3 and C. furcellatus Bailey, clone PMCfl, were isolated by Erik Syvertsen, University of Oslo, on two Pro Mare cruises in the Barents Se:~ in June and July 1984 at about 78°N, 30°E.

Culture medium was made from filtered seawater of 33-35 ppt salinity (collected off Trondhjem Biological Station at 30 m depth) and was enriched according to the "f" recipe of GUILLARO and Rv'rHER (1962) at half strength ("f/2"'). Culture media were pasteurized at 90°C for at least 3 h; bacteria were not observed in Nomarski interference contrast microscopy, Cultures of 1-1 volume were grown in 2-1 polycarbonate bottles and kept at 0.5 + 0.20C in a water bath regulated by a cryostat and two thermostats. The cell density was kept low (30-310 x 103 and 36--450 x 103 cells mi - t of T. nordenskioeldii and C. furcellatus, respectively) by dilution to avoid nutrient deficiency, pH was kept at 8.1-8.7 by bubbling with air.

Modeling light-dependent algal photosynthesis and growth 417

Light was supplied from opposing sides by two banks of six fluorescent tubes each (Philips TL 40W/55). Scalar irradiance was adjusted by neutral nylon screens to 25 or 400/~mol m--" s -~ (PAR), and the cultures were exposed to continuous light or a 12:12 Light: Dark photoperiod. Scalar irradiance was measured inside the bottles with a QSL- 100 photometer (manufacturer: Biospherical Instruments), and spectral distribution outside the bottles with an ISCO Model SR spectroradiometer.

Specific growth rates are given as the average rate predicted by daily monitoring of cell density (determined in a haemocytometer) and in vivo fluorescence with and without DCMU (Turner Designs fluorometer; LORENZEN, 1966) after correction for dilution of the cultures (SAKsHAu6 et al., 1984). Samples for chemical analysis, chlorophyll a (HOLM- HANSEN et al., 1965), P vs I experiments, and determination of dark respiration rates were collected on two different days (2-10 days interval) after the cultures had grown for at least one week. Samples for chemical analysis were collected in duplicate. Filtration, where appropriate, was carried out with baked Whatman GF/C glass fibre filters (50 mb differential pressure). Cellular carbon and nitrogen were analysed in a Carlo Erba Model 1104 Elemental analyser after treatment of the samples with fuming hydrochloric acid.

Filtered (single) samples for determination of pigment composition were extracted overnight at 4°C in the dark with 90% acetone bubbled with nitrogen. Extracts were cleared through GF/C filters and injected onto the column without further treatment. The pigments were analysed by high-performance liquid chromatography (HPLC) on a reverse-phase C-18 column (Brownlee 25 cm × 4.6 mm, 5/~m particles). Pigments were elutcd in a low-pressure gradient system consisting of a linear gradient from 100% A to 100% B in 10 min and maintaining B for another 15 min. Solvent A consisted of 80:20 mcthanol: water (v : v) where lO0 ml of watcr were prepared with 1.5 g of tetrabutylammo- nium acetate (TTAC) and 0.96 g of ammonium acetate (MANTOURA and LLEWELLVN, 1983). Solvent B consisted of 60:4(I methanol:acetate. Pigments were monitored by absorption at 440 nm and quantilicd by calibration of the column with pigments isolated by thin-layer chromatography from a culture of T. nordenskioeldii . Absorption spectra of the clutcd pigments were recorded on a Hitachi Spectrophotometer Model U-2000 fitted with a flow-through cell and compared to published spectra (SrAwER and JEFFREY, 1988).

Chla-spccilic absorption spectra (°at), were measured by collecting samples on GF/C glass tibre filters that were then scanned with a tlitachi Model U-2000 double beam spcctrophotometcr with a wet GF/C filter as a bhmk. Corrections wcrc carried out according to MrrcHEt,e (1987). Fluorescence excitation spectra were determined in a 1 cm quartz cuvette in a Hitachi Model F-3(100 spectrofluorometer at an emission wavelength of 730 nm (NmRI et al., 1988) and a temperature of 0---l°C. Quantum co'rrection was carried out by dividing the raw spectra by the fluorescence excitation spectrum for the dye Basic Bluc 3 in the 400-700 nm range according to KoeF and HEINZE (1984). The quantum- corrected spectra were then scaled by matching of the red peak of the fluorescence excitation spectrum at 676 nm to the corresponding absorption peak °ac. The resulting spectrum °F().~) is in the same units as °ac:

°F(2~x ) = F(2¢x)°ac(676)/°F(676). (i)

The integrated values °a--~ and °--F over 400-700 nm wavelength depend on the spectral composition of the light source and are thus related to PUR (Photosynthetically Usable Radiation, see ~IORE[., 1978). They have been calculated according to the equation

418 E. SAI~sHAUG et at.

2 = X(2)- Eo(2) d2 ,(PAR). IO n m

(2)

where X represents °a e or °F. and Eo(2) and Eo(PAR) represent spectral and total (400-700 nm) irradiance, respectively, of the P vs 1 incubator lamps. We have not corrected for differences in the spectral composition of the light sou___rces between cultures and P vs I studies; the difference is, however, <10% in terms of °ac and °F,

Dark respiration was measured by the Microwinkler Technique. Each culture sample was subdivided into 11 oxygen flasks of 13 mi volume, of which four flasks were analysed for initial oxygen content. The remaining flasks were placed in a black plastic box with crushed ice for incubation. After 10 h, three more flasks were analysed and after 24 h, the remaining four flasks. The results in mg 02 I-l were converted to mg C I" t by assuming a respiratory quotient of 1 : 1 (VErrrv, 1982; LANGOON, 1987).

P vs I experiments were performed at 0.5°C and 10-735/zmol m-2 s- t (PAR), and light was provided from below by an adjustable bank of four fluorescent tubes (Philips TLM 115 W/33RS). Translucent Zinsser polyethylene scintillation vials 20-ml (Cat. No. 307140I) containing I ml of sample were used for incubations. The vials transmitted 99.4 -4- 0.7% of the light. Cell integrity was checked with Evans Blue and was near 100%" e,g. 1.05 times better than in glass vials. Samples were incubated for 1 h at 10:00 h in a photosynthctron (4 x 20 samples), e.g. 2 h into the light phase of the L: D = 12:12 cultures. Total inorganic carbon in the cultures was calculated from Buch's Nomograms on the basis of data for pH. salinity and temperature. Ampoules with I ml of NaHtZCO3, corresponding to 370 kBq (l(lltCi) ml -t (New England Nucle~lr, code NEC-086S), were pooled and tiltercd, and 2 ml was added to 80ml of sample before dispensation into scintillation vials. For determination of total activity, four replicate samples of I ml were immediately dispensed into vials with 30~1 Carbo Sorb (Packard), after which 10 ml of Opti-Fluor scintillation cocktail (Packard) was added.

After incubation, the sample vials were degassed by addition of 0.2 ml of concentrated HCI and shaking for 2 h (LEwiS and SMITH, 1983). After addition of 10 ml Opti-Fluor to each vial, radioactivity was determined in a Packard Tri-Carb scintillation counter Model 3255, and the counts were quench-corrected by means of the External Standard Method, which in turn was checked by the Internal Standard Method (ScmNDLEr, 1966). Counting efficiency ranged from 75 to 85%. The activity of dark bottles was subtracted from the measurements of sample activity, and an isotope discrimination htctor of 1.05 was employed. Regressions on P vs I data were carried out by means of the curvilinear least- square iterative regression program LSQUARE. A list of symbols and units is provided in Table 1.

RESULTS

Growth rate and celhdar compos i t ion

Table 2 summarizes the results of measurements of growth rate and cellular compo- sition. The specific growth rate ranged from 0.09 to 0.33 day- l (0.13--0.48 doubl, day - I ), and the two species exhibited similar responses to the light regime: growth rates at 400/,moi m-" s -t were 2-3 times higher than those at 25,umoi m -2 s -1, and day-length dependence was relatively small. Cellular carbon of Thahtssiosira nordenskioeldi i ranged

Modeling light-dependent algal photosynthesis and growth -1.19

Table I. Symbols and units used in models. Symbols in brackets are used in P vs I models by WEBS et al. (1974). J.assav and PL.~rr (1976) and Pt.Arr et at. (1980)

Eo Scalar irradiance mol m - : h - i . [E,,] Scala- irradiance ,mol m--" s - i . D Day-length h ~ Specific growth rate day- t

• Carbon-specific dark respiration day t °a~ Specific absorption of light m e (mg Chla)- i

°F(.i~0 Scaled fluorescence excitation m-" ( mg Chla) - i spectrum

°o Specific absorption of m 2 ( mg Chla) - i photosynthetically usable light

o Effective absorption cross-section m-" (mol PSU)- t of photosystems

q Chla per photosynthetic unit mg Chla (tool PSU) -t r Minimum turnover time of the h

photosynthetic unit P~ Uptake of carbon g-at C (mg Chla)-t h i [PB I Uptake of carbon mg C (rag Chla)-= h-I [e~l Maximum carbon uptake same as letsl ~I~, .... Maximum quantum yield g-at C (mol photons) i [a" I Photosynthetic efficiency mg C (tug Chla) I h t

(,.molm : s I)-I [/~.] = Pt~l~tn .umol I11 -" s I

• Wc use photon flux instead of energy flux. because the fl~rmer is the more appropri~,tc m photosynthetic equations.

~I '1~, gP~. ~l)m,,,. ~¢t I~, coefficient values normalized to growth rate. The Chla: C ratio is given as nag Chla (g-~,t C) -t (cqul, tion 7) or z,s Img (rag) -t].

from 43 to 6 9 p g c e l l - t and was highest in high con t inuous light. Ce l lu l a r ca rbon in Chaetoceros furcellatus d e p e n d e d mainly on day- l eng th and was 32-47 pg c e l l - t in con- t inuous light and 19-22 pg c e l l - t at 12 h day- leng th . T h e N" C ra t io var ied litt le and ranged from 0.13 to 0.17 ( a toms) for bo th species . C o n s e q u e n t l y , the pa t t e rn of var ia t ion for ce l lu lar n i t rogen was s imi lar to tha t for ce l lu lar ca rbon .

Ce l lu la r ch lo rophy l l a r anged from 1.2 to 3.1 pg c e l l - t for T. nordenskioehli i and from 0.23 to 0.94 pg c e l l - t for C. furcellatus. The lower values pe r t a ined to cells g rown in high con t inuous light. C h l a : C ra t ios exh ib i t ed a s imi lar pa t t e rn o f var ia t ion and ranged f rom 0.018 to 0.065 for T. nordenskioehl i i and 0.008 to 0.036 for C. furcellatus and were sys temat ica l ly 1.7-3 t imes h igher in the fo rmer than in the la t ter . The C h l a : C ra t io was c lear ly day- l eng th d e p e n d e n t at high i r rad iance . Fo r T. nordenskioeldii , the range for the Chic : Chla ra t io was 0 .18-0 .28 mg m g - t ; for C. furcellatus 0.08-0 .70 mg mg - t . Even if Chla pe r cell inc reased f rom light- to s h a d e - a d a p t a t i o n , Chic pe r cell inc reased so s t rongly that the Chic : Chla ra t io inc reased by a fac tor of up to 1.5 in T. nordenskioeldi i and up to 9 in C. furcellatus.

The fucoxan th in : Chla ra t io va r i ed litt le with p h o t o a d a p t a t i o n a l s ta tus ( the obse rva t i on for C. f,~rcellatus in low con t i nuous light is p r e s u m a b l y an ar t i fact ) and was 0 .38-0 .45 mg m g - t for T. nordenskioeldi i and 0 .27-0 .39 mg m g - 1 for C. furcellatus. The ra t io o f the sum of the p h o t o p r o t e c t i v e p igmen t s d i a d i n o x a n t h i n and d i a toxan th in to Chla var ied in oppos i t e fashion to the C h l c : C h l a rat io and reached values up to 0.32 mg mg -~

420 E. SAgSItAt~(; et al.

Table 2. Specific growth rate and chemical and ptgment composition. FL: in vivo fluorescence (relative scale); Fuc: fucoxanthm; Did(: sum of diadino- and diatoxanthin

T. nordenskioeldii C. furcellatus

Eo ..1.I~) 25 4110 25

D 24 12 24 12 24 12 2-1 12 c v.%

u (day -~ ) 1/.33 0.33 O. 12 O. 10 0.311 0.33 0 12 tt.09 5 8

rag(rag Chla) - z FL /).51 (I.41 0.34 11.35 0.77 0.96 0.55 1t,65 IS Chic 11.18 I).22 0.26 0.28 0.08 0. t9 0.N) il,70 20 Fuc 0.411 0,38 0.45 II.43 0.30 11.27 11.39 11.(16 ,'-~ Didi 11.32 f). 10 11.08 11,05 I).77 0.19 11.01 0.07 !~

~g( mg C) - l

Chla 18 -11 65 62 7.9 21 21 36 21 Chic 3.2 9,0 17 17 0.63 4.11 13 25 Fuc 7.2 16 2'4 27 2.4 5.7 8.2 ~ " Did( 5.8 4.1 5.2 3.1 6.1 4.0 0.21 2.5 N(a toms) 1611 1711 Its0 1511 130 1311 160 15(1 7 l)

pg cell i N 13 9. t 4̀.11 7.8 4.~,' 2.`4 8.9 3,8 15 C 6`4 -16 48 43 32 1̀ 4 47 22 t-t Chla 1.2 I.`4 3,1 2.7 I).23 11.3`4 0,`44 0.7`4 ! z

Chic "~ 11.,_ 11.42 (),Sl 0.70 11.112 11.117 [).5('J t).55 Fuc 0,-18 11.72 1,4 1.2 0,07 11, l I 0.37 11.05 l)idi (1.3,~ (). 19 0,25 O. 14 O. 18 0.07 0.01 0.110

for T. nordenskioeMii and 0.77 mg mg-i for C. filrcellatus grown in high continuous light. Shade-adapted cells exhibited low ratios, e.g. 0.0 I--0.08 mg mg -t. Although cells grown in high continuous light might have higher levels of diadinoxanthin + diatoxanthin per cell than other cells, it is evident that a large part of the variation in the Chla-normalized pigment ratio can be explained by the low content of Chla in light-adapted cells.

in vivo light absorption and fluorescence spectra

Chla-specific absorption °a~(2) of T. nordenskioeldii differed considerably between cells grown in high and low light (Fig. 1), as is evident from the readings at 676 and 440 nm (Table 3). Absorption at 676 nm was less than half in shade-adapted than in light-adapted cells. C. furcellatus had generally higher values than T. nordenskioeldii. Scaled fluor- escence excitation spectra °F(2ex ) predicted considerably lower absorption than °ac(2) in the blue region, particularly for light-adapted cells. Thus the difference between light- and shade-adapted cells was smaller in terms of °F(g~x) than in terms of °a¢(2) and, in fact, not evident in C. furceUatus. The integrated value °F(equation 2, Table 3) was only 43-68% of the integrated value °ac.

The FL:Chla ratio (Table 3) represents, in principle, the integrated fluorescence excitation spectrum across the blue region (as defined by the lamp and filter) on a relative

Modeling light-dependent algal photosynthesis and growth 421

~J

E

0 .04

0 03

0.02

0,01

I I

~ n-HL

08 C

I ! 500 (500

m),m I

! !

Tn -LL

! I 5 0 0 e O 0 nm

CI*HL Cf-LL

0.06 08 C 0 8 C

004 , . ,

E 002

_ I I

500 600 500 600 nm

Fig. I. Chla-specific absorption spectra °a~(2), whole lines, and scaled fluorescence excitation spectra *F(2cx ), stippled lines, for light- (HL) and shade-adapted (LL) Thalassiosira nordenskioel-

dii (Tn) and Chaetocerosfurcellatus (Cf) grown at 12 h day-length.

scale. While °F for 12 h day-length was 1.8-2.7 times higher for C. furcellatus than for T. nordenskioeldii, the FL:Chla ratio was 1.9-2.3 times higher, and they form a linear relationship:

°F = 0 .0146(FL: Chla) + 0.0009 (r = 0.938). (3)

As spectra were measured only for 12 h day-length, we have used values for °Fpredicted by equation 3 both for 24 and 12 h day-length in calculations.

4 _ _ E- SAKSHAUG et aL

Table 3. Chla-~pectfic absorption (°a,.) at 676 and 440 nm and scaled excitation fluorescence (°F) at 440 am (the value at 676 n m / s by definition the same as ]or °a<} as well as the integrated values °a¢ and °F (400-700 nm. see

equation 2L Single measurements. 12 h day-length

1". nordensktoldti C. furcellatus

E,, 4(M) 25 4(~) 25

+>a~(676) () 016 0.[~)73 ().03Z 0.02()

~a~(440) 04~ 0.0 [6 ( .063 ()074

°F1440) q).()18 0.()I 1 0.027 0()32

~a~. ().014 0.(X)65 0.024 0.028

"F ().iX)77 0.(X)44 0.014 0.012

°Fl°a~. 0,55 0.68 0 58 (),43

I)ark respiration rates

Hourly carbon-specific respiration rates (rl,) ranged from 0.48 to 3.6 x 10 -3 h ~ and ,~,¢. o/ daily rates (G) from I I t o . o ,,, of the growth n|tc (Table 4). The daily carbon-specific

respiration rate of C. fttrcelhtttts was somewhat lower for cultures growing at a high than at a low rate. and appeared to bc relatively independent of growth rate for T. nordenskioel- dii. Our data support the conclusion by TH.ZER and DUmNS~V (1987) that polar phyto- plankton have extremely low respiration rates on an absolute scale at low temperatures; nevertheless respiration losses may be significant as a per cent of the observed growth rates, as these arc also very low.

[) Vs I cl lrvt '3

The relationship between photosynthesis and irradiance may be described in terms of target theory (ARNOLD, 1932; MYERS and GRAHAM, 1971; LEY and MaUZERAt.L. 19~2; DUmNS~Y et al., 1986; PETERSON et al., 1987; EULERS and PEETERS, 1989). According to the notation by SAKSHAUG et al. (1989), we have that

f 'a = E,, q'm,,x °ac {" [ 1 - e x p ( - orEo) ]/orE,, }, C 4)

where pn is hourly Chla-normalized carbon uptake, Clam,, x is the maximum quantum yield, and °a~ is the Chla-spccific absorption of light. The terms within brackets constitute the Poisson probability that an absorbed photon will hit an open reaction center of a photosynthetic unit; o is the effective absorption cross-section of the photosynthetic unit (functionally defined, e.g. the existence of two different photosystems is disregarded), and r represents the minimum turnover time of the photosynthetic unit.

°a~ and o are spectra which differ both in units and in that °a~ represents all light absorbed by the cells, including that by photoprotective pigments, while o is related to light absorbed by the photosystems, o thus should be the more appropriate spectrum for absorption of photosynthetically usable light and therefore more relevant in models of photosynthesis and growth. We therefore can replace °a,: in equation 3 with a spectral °o in units of m-" (rag Chla) - ~. Thus o may be expressed as q°o, where q signifies Chla per PSU

Modeling light-dependent algal photosynthesis and growth 423

(again. the PSU is functionally defined). Substitution of °o for °ac and q°a for o in equation 4 yields:

pa = (~m~/qr)[1 - exp(-qr°oEo)]. (5)

Equation 5 is mathematically equivalent to the formulation by WEBB et al. (1974). which in turn is equivalent to the formulation by PLA~r et al. (1980) without photoinhibition:

pB = pBm[ 1 _ exp(--Edlk)]. (6)

P~m is the maximum light-saturated photosynthetic rate, and lk equals PBm/aB, where a B is the slope of the curve at the origin. It is easily shown that PB m = 12000 ~max/qr, a B = 73.2 ~m~x°O, and lk = 278/qr°0. Thus a 8 and Ik are, through inclusion of °o, spectrally dependent, while P~ (assuming short-term spectral independence for the product qr) is spectraily independent, in accordance with experimental data (ROCHET et al., 1986). Moreover, a B and PB m include the factor ~m~, while I k does not. Effects of changes in the spectral composition of the light (LEwis et al., 1985; SooHoo et al., 1987) can be taken into account by replacing °o by the integrated value °o (see equation 2).

In equation 5, °ac may serve as one among possible approximations for °o. It has been the commonly employed spectrum in models for algal growth and photosynthesis (KIEFER and MITCHELL, 1983). We have used °F as an alternative, because the fluorescence excitation spectrum at 730 nm emission wavelength closely resembles the shape of the action spectrum for oxygen evolution during photosynthesis (NEoRI et al., 1988).

Fitting of equation 5 to P vs I data yields values for the composite terms ~m~,x°O and cl,,,,,,~/qr (e.g. eta for the P vs I lamps in question and P~m, respectively). ~m~,x as well as the prod t!ct qr can thus be calculated if °o is known. Calculations based on substitution of °F for °(1 yield values for ~l~,,~,,x of 0.045-0.088 (T. nordenskioeldii) and 0.019-0.060 (C. J'urcellams, Table 4). Calculations on basis of °a~ would on average yield values for ~m~x that are 44% lower, e.g. 0.010--0.050. These wide ranges are due to aberrantly low values for cl~,,,,,x of cultures grown in strong continuous light, which in turn are reflected in correspondingly low values for P~, and a u (Table 4). Values for ~m,~ for the 0thor light regimes averaged 0.077 for T. nordenskioeldii and 0.055 for C. furcellatus when based on °F, and about 0.04 and 0.03, respectively, when based on °a c. Values for the product qr calculated on the basis of the product qr°o(= l/lk) and substitution of °F for °o were about 2-3 times higher for cultures grown at low than at high irradiance, and values for T. nordenskioeldii were systematically 1.6-2.9 times higher than values for C. furcellatus. Values calculated on basis of °a~ would, on average, be 44% lower; e.g. 135-870 instead of 240--1550.

Normalization to the gross growth rate

The gross carbon-specific growth rate can be described by P vs 1 formalism by multiplication of such a function with the Chla:C ratio and day-length. We suggest a modification of the model by SAKSHAUG et al. (1989) based on equation 5:

~ + r = (Chla:C)D(g~max/qr)[l -- exp(-qr°oEo)], (7)

where l~ and r are the carbon-specific growth and respiration rates, respectively (day- t ). D is day-length, and g'~.,.x is a growth-normalized value of ~m.~- The normalization of only Cm,,x to growth is convenient and logical: <l)m. ~ depends on the method for measurement of

424 E. SAKSH^UG et at.

photosynthesis (oxygen release vs carbon uptake, filtered vs unfiltered samples). In the terms of equation 6 this means retaining lk and changing a B and P~.

Gross growth rates predicted on the basis of equation 7 and the original P vs 1 coefficients (u + r)* generally differed from the observed rates (u + r) and thus imply different values for e'(l)~.~ and ~m,,, (Table 4). The predicted rates were higher than the

Table 4. Respiration rates, P vs 1 coefficients, gross growth rates and growth-norrnalized P v~ I {'oefftci~'nts

T. nordenskioeldii C. furcellattL~

Eo 41~1 25 4111 _~'~-

D 24 12 24 12 24 12 24 12

r , x 10 ~ 2.9 1.5 1.3 2.4 3.6 2.8 1.7 I}.48

r,, (%} 21 11 27 56 29 21 35 t3

~bm,,, x [f}3 45 71 88 73 19 45 N) t',(I

°F x 103 8.4 6.9 5.9 6.0 12 15 8.t, ~ t()

qr 71~1 6311 1551} 141~1 241} 33(} 8ql~ SN)

P~ 11.76 1.3 11.71} 0,64 1.11 1.7 11.84 11.87

+t n x 11) 3 16 21 . . . . ~ 19 10 "~g 23 -,"r,

I~, 4~ {+5 31 33 I (It) 5g 36 32

!t + r 0.411 t}.37 11.15 0.16 11,39 11.411 II. 11~ {I. 1t1

(,it + r) ° 11.31 il.64 IJ.6l 11.2() 1t.211 11.42 "~ I),21

~t) ...... x 11} ~ 58 41 22 45 37 43 44 2~ g It P., {}.t)N 11.75 11.17 11.39 1.95 1.6 0.()1 11.4i

~(t n x I(¢ 21 12 5.4 12 2(1 28 17 13

~ . v . %

IS

i.3

rh is carhon-specil ic dark rcspiratit)n (h - I ) , r , is daily loss tff carbtm ( = 24r h) as per cent of the specilic gn,v.th rate. ,u + r: measured gross growth rate (r = 24 rh); (/+ + r)°: gross growth rate predicted by the original P vs / coefficient values and the C h l a : C ratio through equa t ion 7.

Table 5. Average values for gross growth rate. growth.normalized photosynthetw coefficients and pigment composition o f Thalassiosira nordenskioeldii and

Chae toceros furcellatus

E . 411~ 25

D 24 12 24 12

!+ + r 0.411 0.39 0.16 o. 13

°F 0.1111} 1L1)11 0.b~)74 ().(J082

~ql)m~ ~ x I(¢ 48 42 33 37

q r 3911 4211 11)711 11)91} 1~ )1! t m 1,5 1.2 0.39 0.40

g(£t~ x 10 ~ 21 211 11 13

1~, 71 60 35 31

Chla : C x l ip 13 31 43 4*;

Chic: Chla 0.13 0.2 t 0.43 0.49

Fuc: Chin 0.35 11.33 1142 - -

Didi : Chla 0.55 11.15 0.115 ().IR~

Mu-deling light-dependent algal photosynthesis and growth 425

observed ones, which implies a lower value for gq)max than for ~,~a~, except for the converse result for cultures grown in continuous high light. The growth-normalized coefficients gpa and ga B differ from p a and a B in apro rata fashion (Table 4). g~,,~ varied without apparent pattern and was (ba_ sed on °F) 0.042 for T. nordenskioeldii and 0.038 for C. furcellatus. Predicted on basis of °a c g~,~a~ would, on average, be 44% lower, e.g. about 0.023.

DISCUSSION

Photoadaptation in two Arctic diatoms

Photoadaptive variation in photosynthetic parameters depends mainly on irradiance and little on day-length. The pigment composition depends, however, both on irradiance and day-length, and the effect of day-length is pronounced at high growth irradiance (Table 5).

The difference between species in terms of growth and photosynthetic coefficients may be easily summarized, because growth rate, lk, ~ruax, and t~ma x exhibit no systematic differences between the two species, while Pa m, a B. their growth-normalized counterparts, and °F and the product qr are systematically higher for C. furcellatus than for T. nordenskioehlii. The Chla:C ratio varies, however, inversely. This relationship between the Chla:C ratio on one hand and °F and the product qr on the other yields a similar pattern of variation for the gross growth rate for the two species.

Spccitic light absorption (°a~) is considerably lower in shade- than in light-adapted cells of T. nordenskioeldii. Part of this difference is presumably due to the packaging effect (KIRK, 1975; BRICAUD et al,, 1983; GF, IDI.~R and OSBORNF, 1987; MITCIlF, I.I, and KIF, FER, 1988a; BrRNEr et al,, 1989). C. furcelhaus exhibits less photoadaptation-depcndcnt variation, but °a~. is extremely high, which in turn results in a high °F. We do not believe the high °F is an artifact of the procedure, because the treatment and sample density on the liltcrs wcrc the same as for T. nordenskioehlii, which yields expected results.

Thc two species also differ in that C. furcellatus exhibits an extremely wide range for the Chlc:Chla ratio relative to T. nordenskioeldii, and the former also appears to contain morc photoprotcctivc pigments in strong continuous light. Thus C. furcellatus is more plastic in terms of pigment regulation than T. nordenskioeldii. The high proportion of photoprotcctive pigments (strong light only) and Chic in C. furcellatus may contribute to a high °a¢ in this species; Chic may also contribute to a high °F. The little variation in the fucoxanthin:Chla ratio has been reported for Skeletonema costatUm (FALKOWSKI and OWENS, 1980).

The model

We have introduced a modified version (equation 7) of the model by SAKSHAUG et al. (1989). It differs from the earlier version (equation 4) by having one spectrum (°o), which expresses the Chla-specific absorption of photosynthetically usable light. This factor incorporates into calculation variations in the short-term spectral variation in light. We think that the notation of the modified model is more relevant in terms of physiology than other models commonly employed in marine research. It contains explicitly the absorption of photosynthetically usable light by phytoplankton, and it is convenient for the study of

426 E. SAXS~UG et al.

species-specific strategies, because it expresses differences in such strategies as differences in the pattern of variation in physiologically relevant coefficients.

Considered as a P vs I function, equation 5 assumes no photoadaptive change in the coefficients during the course of a measurement. Even for an incubation time as short as one hour this may not be true (Lewis and SmrrH, 1983). Cyclic transport may occur between PSI and PSII (DumNsKY et al., 1986), variations in energy transfer between PSII reaction centers may occur (HERRO~ and MAUZ~:RALt., 1972), and r or the product qr may increase due to inactivation of reaction centers as a response to the high irradiances (BPaANtAIS et al., 1988; NEAL~: and Meets, 1990). We believe that target theory represents the basic formulation for the P vs I relationship, but acknowledge that physiological changes taking place during incubation may modify the P vs I curve so that certain empirical functions may yield a better fit to data (JASSBr and Pt.arr. 1976; PriouL and CHARaaER, 1977; LEvEr~NZ, 1988).

A limitation of the present model is the lack of a photoinhibition parameter. In the present case photoinhibition is negligible; for example lbsensu Pt.A~retal. (1980) is as high as 2400-5200,umol m-2 s- t (G. JOHNSEN. unpublished data), while irradiance in Arctic waters does not surpass 1000/zmol m-" s -l. Photoinhibition may, however, be included in the model by letting r or the product qr increase with irradiance as a short-term response

Pro). for which there is supportive evidence (BRIANTAIS et al.. (thus gradually reducing 13 1988). A simple expression for r or qr as a function of E,,. however, would prcsumably bc overly simplistic from a physiological point of view (NeAt.e and MELZS, 1990) and would not cover changes in photoinhibition with incubation time or spectral changes in light.

Results f rom the model

Calculations of ~D,n,,,, based on °a,: yield markedly lower values than calculations based on °F. The range of 0.05 to 0.08 for Clam,, x predicted on basis of °F is realistic for carbon uptake when nitrate is the nitrogen source (see LANC;OON, 1988). Admittedly, the present values may be on the low side, because of mitochondrial respiration during the lighting period and_, thus, r may have been underestimated (Wet;er et al., 1989). Values for ~D,,~,~ based on °a,: are, however, implausibly low, e.:g. 0.03-0.045. We thereforc conclude that "F is the more appropriate approximation for %r.

Because a lower value for ~,,,,,x than for t~m,~, , is unlikely, values of ,D,,,~,, for cultures grown in strong continuous light are presumably erroneous. These cultures were probably under considerable stress (cf. very low Chla:C ratios and high respiration rates); thus additional stress due to manipulation in conjunction with P vs 1 experiments may have brought the algae close to their limit of tolerance. Apart from the results in strong continuous light, e'~m,, ~ is, on average, 30--45% lower than • .... which exceeds that expected by extraceilular production. Although this process is highly species-dependent (M','~LnSTAO, 1974), it usually constitutes <10% of total carbon fixation in nutrient- sufficient phytoplankton (Foe;a, 1983; ZLO'rNIK and DomNsKe, 1989). A similarly large difference in terms of carbon uptake has been observed in P vs / studies by comparison of filtered and unfiltered samples from parallel experiments with phytoplankton from Auke Bay, Alaska (CONQUESt, 1986; ZleMAN~ et al., 1987). This large discrepancy as well as other features regarding the variability in ~r,,,,,,, implies that further research is important if we are to understand the relationship between photosynthesis and growth. One should also bear in mind that a comparison of cb,,,,,,~ derived from a P vs I curve obtained at a

Modeling light-dependent algal photosynthesis and grov,th 427

specific time with g~,,,~,,, may be complicated by the diurnal variation in P vs I coefficients (LEGENDRE e t al.. 1988).

The product qt increased by a factor of 2-3 from light- to shade-adaptation: accordingly gPB m and lk decreased, as was also observed for Thalassiosira psettdonana by LEWIS and SMITH (1983). The high covariation between pB and a B in boreal and Arctic waters (HARRISON and PLATr, 1980. 1986) may be explained by the concomitant decrease in °aand the increase in the product qr from light- to shade-adaptation. Both q and r increase from high to low light (DuBINSKV et al., 1986). The factor q may be influenced by the size of both PSI and PSII. We have neglected interactions between the two photosystems in our models because we have not carried out relevant measurements: a comparison, however, of q for S. costatum (M. GILSTAD, unpublished data) with Chla/PSU of other species (DuBINSKV et at.. 1986) all grown at 15°C. indicates that q corresponds well to the size of PSII and is much smaller than the size of PSI.

The product qr of 630-|550 mg Chla h (mol PSU) -1 for T. nordenskioehlii grown at (I.5°C is much higher than values for T. weissflogii grown at 15°C ( 150-500 based on PSII: DUBINSKY et ~d., 1986). This indicates that r or q or both decrease when temperature increases. This explains thc increase in P~ with increasing temperature (HARRISON and P LAI'I, 1986).

A l~plications o f tile model

The use of °F may be of advantage in the tield, because it is affected little by dctrital intcrfcrence (MASKF. and HAAR|)T, 1987) and it corrects for absorption by photoprotective pigments. The scaling procedure requires qt, antunl correction in the entire visible range. which has been diflicult to achieve (MrrcHF, I.t. and KII-FI~.R, 1988b), but now can bc carricd out conveniently (KoPl: and [-[EINZE, 1984). The scaling also requires knowledgc of the red peak of °,~.. Fortunately, this part of °~1~ is the least intlucnccd by detritus with the cxccption of phaeopigments. Temperature dependence of the fluorescence spectrum is of no consequence for the scaling procedure as long as the shape of thc spectrum remains the same. Albcit imperfect and possibly somewhat overestimating °~i, °F therefore may be the better and more convenient approximation for °¢I also in the lield, while °a~. (with detritus included) is the relevantspectrt(m for modeling of the submarine light regime. It is likclv their the ratio between °F and °~t~ (Table 3) is lower in blue oceanic waters than for thc "'white" incubator lights used here, particularly for light-adapted cells, because of their high content of photoprotectivc yellow pigments.

As calculations taking spectral information into consideration are considerably more laborious than calculations based on PAR, one may raise the question as to what extent such an undertaking is worth the effort. According to model studies of algal growth in a rapidly mixed and homogeneous surface layer, the choice of PAR vs PUR models is of little consequence in shallowly mixed columns, but the difference between PUR- and PAR-based predictions for integrated primary production or the timing of a spring bloom becomes increasingly large as the depth of the mixed water column increases, and particularly so when the difference between growth and losses (sum of respiration, cxtraccllular production, sedimentation and grazing) is small (SAKSHAUG and SLAGSTAD. in press). This is actually evident from inspection of P vs I curves: Because l'I~, is spcctrally indcpcndent, predictions of primary production or the algal growth rate for strong light (shallow mixing) should bc nearly spectrally independent: conversely, in weak light (deep

428 E. S~acs~uG et al.

mixing) the predictions will be affected by the spectrally dependent and thus vertically variable value a B. Spectral information may therefore be important for modeling of photosynthesis and algal growth in open waters where deep mixing is prevalent. Finally, along the Norwegian Coast where dissolved humic matter, mainly of Baltic origin, makes the water distinctly green, even when the phytoplankton stocks are at their smallest, "algae are exposed to a fight regime which is qualitatively very different from that of the adjacent blue North Atlantic waters. Because of this, a a may be systematically lower in coastal than in North Atlantic waters.

Acknowledgements~This work is part of Pro Mare (The Norwegian Research Program for Marine Arctic Ecology) and was supported by the Norwegian Research Council for Science and the Humanities (NAVF) through grants to E. S., including financing of a sabbatical at Trondhjem Biological Station for M. V. Thanks are due to an anonymous referee and Dr Paul Biehfang for constructive criticisms and to Mr Lars Harald Vik for assistance in developing programs for processing of spectra. The data for chemical composition, growth and respiration rates, and P vs I curves were used by G. J. for his cand. scient, (M.Sc.) thesis. Contribution 246, Trondhjem Biological Station.

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