Deep-Sea Re~earch. Vol. 38. No. 4, pp. 415--4311. 19ql.
0198-0140/91 $3.011 -*- 0.fin
~ lt~O[ Pergamon Prexs plc
Prmted ill Great Bntam.
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 SAKSHAUGet al. (1989, Limnology and Oceanography. 34. 198-205) and
WEBBet 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 lightadapted 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~mand 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.
INTRODUCTION
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;Get 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; GEnDeRet al.,
1986; SAKSHAUGet al., 1989). The model by SAKSHAtJGet 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 combinations 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 SAKSHAUGet al. (1989) to Arctic phytoplankton. Few investigations 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 SAKSrlAUGet 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 GUILLAROand 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.
Modelinglight-dependentalgal photosynthesisand 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 QSL100 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 (HOLMHANSEN 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 tetrabutylammonium 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 quantumcorrected 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 °--Fover 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~sHAUGet at.
2 =
X(2)- Eo(2) d2
,(PAR).
(2)
IO n m
where X represents °ae 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___rcesbetween 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 leastsquare iterative regression program LSQUARE. A list of symbols and units is provided in
Table 1.
RESULTS
G r o w t h rate a n d celhdar c o m p o s i t i o n
Table 2 summarizes the results of measurements of growth rate and cellular composition. 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 nordenskioeldii 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
WEBSet al. (1974). J.assav and PL.~rr(1976) and Pt.Arr et at. (1980)
Eo
[E,,]
D
~
•
°a~
°F(.i~0
~I~,....
[a" I
Scalar irradiance
Scala- irradiance
Day-length
Specific growth rate
Carbon-specific dark respiration
Specific absorption of light
Scaled fluorescence excitation
spectrum
Specific absorption of
photosynthetically usable light
Effective absorption cross-section
of photosystems
Chla per photosynthetic unit
Minimum turnover time of the
photosynthetic unit
Uptake of carbon
Uptake of carbon
Maximum carbon uptake
Maximum quantum yield
Photosynthetic efficiency
[/~.]
= Pt~l~tn
°o
o
q
r
P~
[PBI
[e~l
mol m - : h - i .
,mol m--" s - i .
h
day- t
day t
me (mg Chla)- i
m-" ( mg Chla) - i
m2 ( mg Chla) - i
m-" (mol PSU)- t
mg Chla (tool PSU) -t
h
g-at C (mg Chla)-t h i
mg C (rag Chla)-= h-I
same as letsl
g-at C (mol photons) i
mg C (tug Chla) I h t
(,.molm : s I)-I
.umol I11-" s I
• Wc use photon flux instead of energy flux. because the fl~rmeris the more appropri~,tc m
photosynthetic equations.
~I'1~,gP~. ~l)m,,,. ~¢tI~, 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 a n d was highest in high c o n t i n u o u s light. C e l l u l a r c a r b o n in
Chaetoceros furcellatus d e p e n d e d m a i n l y on d a y - l e n g t h a n d was 32-47 pg c e l l - t in cont i n u o u s light a n d 19-22 pg c e l l - t at 12 h d a y - l e n g t h . T h e N" C ratio v a r i e d little and r a n g e d
from 0.13 to 0.17 ( a t o m s ) for b o t h species. C o n s e q u e n t l y , the p a t t e r n o f v a r i a t i o n for
c e l l u l a r n i t r o g e n was s i m i l a r to t h a t for c e l l u l a r c a r b o n .
C e l l u l a r c h l o r o p h y l l a r a n g e d from 1.2 to 3.1 pg c e l l - t for T. nordenskioehlii and from
0.23 to 0.94 pg c e l l - t for C. furcellatus. T h e l o w e r values p e r t a i n e d to cells g r o w n in high
c o n t i n u o u s light. C h l a : C r a t i o s e x h i b i t e d a similar p a t t e r n o f v a r i a t i o n a n d r a n g e d from
0.018 to 0.065 for T. nordenskioehlii a n d 0.008 to 0.036 for C. furcellatus a n d w e r e
s y s t e m a t i c a l l y 1.7-3 t i m e s h i g h e r in the f o r m e r t h a n in the latter. T h e C h l a : C r a t i o was
clearly d a y - l e n g t h d e p e n d e n t at high i r r a d i a n c e . F o r T. nordenskioeldii, the r a n g e for the
C h i c : C h l a ratio was 0 . 1 8 - 0 . 2 8 m g m g - t ; for C. furcellatus 0 . 0 8 - 0 . 7 0 mg m g - t . E v e n if
C h l a p e r cell i n c r e a s e d f r o m light- to s h a d e - a d a p t a t i o n , Chic p e r cell i n c r e a s e d so s t r o n g l y
that the C h i c : C h l a ratio i n c r e a s e d by a factor o f up to 1.5 in T. nordenskioeldii a n d up to 9
in C. furcellatus.
T h e f u c o x a n t h i n : C h l a r a t i o v a r i e d little with p h o t o a d a p t a t i o n a l status (the o b s e r v a t i o n
for C. f,~rcellatus in low c o n t i n u o u s light is p r e s u m a b l y an artifact) a n d was
0 . 3 8 - 0 . 4 5 mg m g - t for T. nordenskioeldii a n d 0 . 2 7 - 0 . 3 9 mg m g - 1 for C. furcellatus. T h e
r a t i o o f the sum o f the p h o t o p r o t e c t i v e p i g m e n t s d i a d i n o x a n t h i n a n d d i a t o x a n t h i n to Chla
v a r i e d in o p p o s i t e fashion to the C h l c : C h l a ratio a n d r e a c h e d values up to 0.32 mg m g -~
420
Table 2.
E. SAgSItAt~(; et al.
Specific growth rate and chemical and ptgment composition. FL: in vivo fluorescence (relative scale);
Fuc: fucoxanthm; Did(: sum of diadino- and diatoxanthin
T. nordenskioeldii
Eo
D
..1.I~)
24
C. furcellatus
25
12
24
4110
12
24
25
12
2-1
12
u(day-~)
1/.33
0.33
O. 12
O. 10
0.311
0.33
0 12
tt.09
rag(rag C h l a ) - z
FL
Chic
Fuc
Didi
/).51
11.18
0.411
11.32
(I.41
I).22
0,38
f). 10
0.34
0.26
0.45
11.08
11.35
0.28
II.43
11,05
0.77
0.08
0.30
I).77
0.96
0. t9
11.27
0.19
0.55
0.N)
11.39
11.01
1t,65
il,70
11.(16
0.07
~g( mg C) - l
Chla
Chic
Fuc
Did(
N(atoms)
pg cell i
N
C
Chla
Chic
Fuc
l)idi
18
3.2
7.2
5.8
1611
13
6`4
1.2
11.,_
"~
0,-18
(1.3,~
-11
9,0
16
4.1
1711
9. t
-16
I.`4
11.42
11.72
(). 19
65
17
2'4
5.2
Its0
`4.11
48
3,1
(),Sl
1,4
0,25
62
17
27
3.1
1511
7.8
43
2.7
0.70
1.2
O. 14
7.9
0.63
2.4
6.1
130
4.~,'
32
I).23
11.112
0,07
O. 18
21
4.11
5.7
4.0
1311
2.`4
1`4
11.3`4
11.117
11, l I
0.07
21
13
8.2
0.21
160
8.9
47
0,`44
[).5('J
0.37
0.01
c v.%
58
IS
20
,'-~
!~
36
25
~"
2.5
15(1
21
3,8
15
t-t
!z
22
0.7`4
t).55
11.05
0.110
7 l)
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 fluorescence 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-dependentalgal photosynthesis and growth
I
~
0.04
m),m
n-HL
I
!
Tn -LL
08 C
0 03
~J
!
I
421
0.02
E
0,01
I
!
!
I
500
(500
500
eO0
CI*HL
nm
Cf-LL
0.06
08 C
08 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 nordenskioeldii (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 a m (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
E,,
4(M)
C. furcellatus
25
4(~)
25
+>a~(676)
~a~(440)
°F1440)
() 016
04~
q).()18
0.[~)73
0.0 [6
0.()I 1
().03Z
( .063
0.027
0.02()
()074
0()32
~a~.
"F
°Fl°a~.
().014
().iX)77
0,55
0.(X)65
0.(X)44
0.68
0.024
0.014
0 58
0.028
0.012
(),43
I)ark respiration rates
Hourly carbon-specific respiration rates (rl,) ranged from 0.48 to 3.6 x 10 -3 h ~ and
daily rates (G) from I I t o . ,~,¢.
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. nordenskioeldii. Our data support the conclusion by TH.ZER and DUmNS~V (1987) that polar phytoplankton 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 v e r y low.
[) Vs I cllrvt'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; PETERSONet al., 1987; EULERSand PEETERS, 1989). According to the
notation by SAKSHAUGet al. (1989), we have that
f 'a = E,, q'm,,x °ac {"[ 1 - e x p ( - orEo) ]/orE,, },
C4)
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 photosynthesisand 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 WEBBet 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~mis 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 PBm = 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 PBm 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 SAKSHAUGet 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^UGet 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
Eo
41~1
D
24
r, x 10~
25
12
2.9
C. furcellattL~
24
1.5
4111
12
1.3
2.4
r,, (%}
21
11
27
56
~bm,,, x [f}3
45
71
88
8.4
71~1
6.9
6311
5.9
1551}
°F x 103
qr
19
45
N)
t',(I
6.0
141~1
12
241}
15
33(}
. 19
I~,
4~
{+5
31
33
t}.37
11.15
il.64
IJ.6l
g
58
P.,It
{}.t)N
~(t n x I(¢
21
41
1.11
.
5.4
11,39
1t.211
12
11.84
23
11.87
-,"r,
5g
36
32
II. 11~
"~
43
1.95
2(1
i.3
I),21
2~
0.()1
28
IS
{I. 1t1
44
1.6
~.v. %
t()
SN)
"~g
11.411
11.42
37
11.39
8.t,~
8ql~
1.7
10 .
I (It)
45
11.17
12
0,64
0.16
11.2()
22
11.75
I}.48
73
11.71}
11.31
1.7
t3
~.
0.411
2.8
12
35
1.3
21
(,it + r) °
3.6
24
21
11.76
16
!t + r
_~'~12
29
P~
+tn x 11)3
~t) ...... x 11}~
24
17
11.4i
13
rh is carhon-specilic 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: m e a s u r e d gross g r o w t h 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 e q u a t i o n 7.
Table 5. Average values for gross growth rate. growth.normalized photosynthetw
coefficients and pigment composition o f Thalassiosira nordenskioeldii and
C h a e t o c e r o s furcellatus
E.
D
411~
24
0.411
25
12
!+ + r
°F
~ql)m~~ x I(¢
48
0.39
1L1)11
42
qr
0.1111}
24
0.16
0.b~)74
33
11)711
12
o. 13
().(J082
37
3911
4211
1~ )1!
t m
g(£t~ x 10~
1,5
21
1.2
211
0.39
11
11)91}
0.40
13
1~,
71
60
35
31
Chla : C x lip
Chic: Chla
Fuc: Chin
Didi : Chla
13
0.13
0.35
0.55
31
0.2 t
11.33
11.15
43
0.43
1142
0.115
4*;
0.49
-().IR~
Mu-delinglight-dependent algal photosynthesisand 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 °ac 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 Pam, 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; BRICAUDet al,, 1983; GF,IDI.~Rand 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 SAKSHAUGet 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~UGet 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
(thus gradually reducing Pro).
13 for which there is supportive evidence (BRIANTAISe t al..
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 from 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 nutrientsufficient phytoplankton (Foe;a, 1983; ZLO'rNIKand 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
Modelinglight-dependentalgal photosynthesisand grov,th
427
specific time with g~,,,~,,, may be complicated by the diurnal variation in P vs I coefficients
(LEGENDREe 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 LEWISand
SMITH (1983). The high covariation between pB and a B in boreal and Arctic waters
(HARRISONand 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 (DuBINSKVet 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 (HARRISONand
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 (SAKSHAUGand 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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