Presentation number: OS42H-184

Nonlinear modelling of the coupling between carbon and nitrogen pathway during phytoplankton growth. Validation with chemostat experiments on Rhodomonas salina. Lionel Pawlowski,

INSU

Emilie Le Floc’h,

Antoine Sciandra

Olivier Bernard

LOV, CNRS/UPMC/OSU, UMR7093, Station Zoologique, La Darse , B.P.28, 06234 Villefranche sur Mer, France

INRIA, Projet COMORE, 2004 route des Lucioles, B.P.93, 06902 Sophia-Antipolis, France

Simulation vs. Experimental data

Model equations

Abstract We propose a nonlinear model to describe the light- and nitrate-limited phytoplankton growth. The model incorporates the coupling between carbon and nitrogen metabolic pathways. Its complexity (4 variables and 8 parameters) remains compatible with mesoscale carbon ux computations, and guarantees that it can be incorporated in 3-D NPZ models. The main hypothesis of the model is that the effect of light on chlorophyll synthesis may be deregulated by a nitrogen deciency. The model, based on mass balances, has been validated with chemostat experiment data, in two steps. First its qualitative behaviour has been studied independently from the parameter values. The responses of computed steady states to an increase in light and/or dilution rate have been compared to experimental observations. The study has also been reinforced by the trend analysis for ratios between nitrogen, carbon and chlorophyll. The model is qualitatively in agreement with the data. The parameter values have then been identied by subsets, on the basis of the experimental steady input-output behaviour which provides linear regressions. In a last step the model has been quantitatively validated using dynamic chemostat experiments performed with Rhodomonas salina simultaneously limited by light and nitrate in a computer controlled culturing device.

Parameters

Effect of light on chlorophyll a synthesis

Differential equations

Chlorophyll synthesis rate is a function of light (k(I)) and of the nitrogen to carbon ratio. In ne, it reproduces the photoadapation process.

kl ⋅ kc k (I ) = kc + I

S & S = d ⋅ Sin − S − m ⋅ ⋅ C ( ) ρ  S + ks   N& = −d ⋅ N + ρm ⋅ S ⋅ C − a ( I ) ⋅ k ( I ) ⋅ N ⋅ L + β ⋅ L  C S + ks   L &  L = −d ⋅ L + a ( I ) ⋅ k ( I ) ⋅ N ⋅ − β ⋅ L C  C& = −d ⋅ C + a ( I ) ⋅ L − λ ⋅ C Net carbon incorporation rate

Photosynthesis rate

a( I ) =

Photosynthesis rate is an increasing function of light with a Monod kinetics and of the chlorophyll to carbon ratio.

α ⋅I ki + I

I: light intensity (µmol quanta.m-2.s-1)

Sin: nitrate supply (µM N) d: dilution rate (d-1)

Values

Units -1

ρm

0.5

ks

0.43

µM N

kl

6.59

n.d.

kc

33.0

µmol quanta.m -2.s-1

α

24.1

d

ki

208.5

µmol quanta.m .s

β λ

0.054 0.345

d-1 -1 d

µmol N.µmol C .d

For dynamic simulations, parameters values were estimated from experimental data using linear regressions based on transformation and combination of steady-state solutions (see Pawlowski et al., 2002 for details on the used method).

-1

The model is then integrated with a second order Runge-Kutta method with variable step time.

-1 -2

-1

Dynamic simulations show that carbon and chlorophyll predictions are close to observations. Transient phases evolve accordingly to the experimental data. Carbon predictions are closer to measurements than chlorophyll predictions.

Parameters values of the model for Rhodomonas salina cultures in chemostat at 19°C.

Keywords: Modeling, Photosynthesis, Phytoplankton, Nitrogen limitation, Multiple limitations, Photoadaptation, Chemostat, Carbon cycling 120

Extracellular Nitrogen (Nitrate) S

À

Extracellular Carbon

Light lumiËr e

- Non limiting extracellular carbon is incorporated into the cell through photosynthesis and forms particulate carbon (state variable C). Photosynthesis depends positively (green dashed arrows) on light intensity and on the amount of chlorophyll a pigments (state variable L).

Non-chlorophyllian Particulate nitrogen N Pigments degradation

(-) Chlorophyll synthesis

Carbon incorporation into the cell. - Phytoplankton growth is the result of the balance between carbon xation and respiration.

Absorption

Â

Parameters

Á

Á

À

(+)

Chlorophyll a L

Symbols

Maximum uptake rate

ρm

Half saturation constant for nitrate absorption

ks

Maximum chlorophyll synthesis rate

kl

Threshold coefficient for chlorophyll synthesis

kc

Maximum carbon fixation rate

α

Half saturation constant for carbon fixation

ki

Pigment degradation rate Respiration rate

β λ

Particulate Carbon

Â

C

Respiration

- Only 8 parameters are used allowing an easier identication of model parameters.

Model qualitative properties

Steady-state Light variable intensity I C* L*

- Proteins associated with chlorophyll are produced from the cellular nitrogen pool (state variable N) where the sources are the absorption of extracellular nitrate (state variable S) and the degradation and recycling of chlorophyll pigments.

N* N*:C*

Conceptual schema : plain arrows represent nitrogen uxes

L*:C*

between pools S,N,L and carbon ux towards pools C.

- Net carbon incorporation rate may be directly estimated from the carbon equation.

dilution rate d

Ê Ì Ê Ì Ì&Ê

Ì Ê Ì Ê Ê

- Carbon concentration increases with light and decreases with dilution rate (Geider et al., 1998). - Chlorophyll concentration is a decreasing function of light due to photoadaptation (Laws and Bannister, 1980) and increases with the dilution rate. - Chl:C ratio increases with the dilution rate and decreases with light intensity (Chalup and Laws, 1990; Geider et al., 1998; Falkowski and Raven, 1997). - N:C increases with the dilution rate (Chalup and Laws, 1990) and decreases with light.

Particle Analysing System Nutrient Pump pH

T°C pH

solenoid valves

pH pH

CO2

3

2

1

Nutrient Medium

pH Regulating / T°C acquisiting System

750

500

250

0

12 10 8

estimated by a spectrophotometric method (not shown in the diagram). Concentration of particulate nitrogen and carbon are obtained by a CHN analyzer. Residual substrate (nitrate) concentration is measured by an automaton connected to a TECHNICON auto-analyzer. See Bernard et al., 1996 for more details.

60 40 20

10

20

30

0

40

10

0,1

0,2

Dilution rate (day-1)

0,3

0,4

30

40

Time (days)

Conclusions - This model comprises simple assumptions and has few parameters. Because of the low dimension, a mathematical analysis is possible and reveals that model properties are simple. The absence of quota state-variables permits the integration of this system in more complex multidimensional models (trophic network). - In some cases, simulations are not close to observations. To improve this model, the following hypotheses may be reconsidered: 1) Chlorophyll a complexes have a constant proportion of nitrogen (apoproteins). 2) Carbon xation per chlorophyll a is considered as constant (invariant absorption and quantum yield). 3) Chlorophyll a degradation is a constant.

Number of

Number of

state variables

parameters

Limitations

Explicitely used quotas growth rate

Photo-

Growth compensating

adaptation

phenomenon

Flynn, 2001

13

55

light, multinutrient, temperature

variables & parameters

Geider et al. , 1998

4

12

light, nitrate, temperature

parameters

yes

yes

yes

Zonneveld, 1998

5

14

light, nutrient

no

no

yes

no

Pawlowski et al., 2002

4

8

light, nitrate

no

no

yes

yes

yes

yes

yes

limitations, the use of quotas as state-variables or parameters, of growth rate parameters, the integration of the photoadaptation process (chlorophyll concentration to carbon ratio decreasing as light intensity increases) and of the growth compensating phenomenon (nitrogen to carbon ratio decreasing as light intensity increases).

6 4 2

References

0 0

20

Comparison between this model and other recent phytoplankton growth models according to the number of state-variables, parameters, featured growth

0

0,1

0,2

Dilution rate (day-1)

0,3

0,4

Nutrient Supply System

Synoptic diagram of the culturing and acquisition systems. The cell density is acquired with an automated laser HIAC particle counter. Chlorophyll a is

80

0

14

Chlorophyll a (µM N)

solenoid valve

1000

Particulate carbon (µM C)

System Filtering

Nutrient Analysis System

Airflow

0

Reference

DILUTOR

100

- The model has been mainly validated at steady-state. Further experiments are necessary to reproduce dynamic conditions of light and nitrogen (photoperiod, mixed layer) that trigger the photoacclimation in a non linear way.

TIMER HIAC COUNTER

d=0.1

experiment is 32 µmol quanta.m-2.s-1. The dilution rate is successively set to 0, 0.3 and 0.1 d-1.

Conclusion: Model behaviour is consistent with each of these observations.

Culturing and acquisition systems

NITRATES Auto-Analyzer

250

d=0.3

Comparison of experimental data (red +) and model output (solid line) for particulate carbon and chlorophyll a. Light intensity during the

Experimental observations:

of model state variables and of N:C and Chl:C ratios.

NITRITES

d=0.1

Mathematical analysis of model solutions at steady-state shows that, independently from the parameter values, trends of variables measured for combined rates of light and dilution are in agreement with those calculated by the model.

Summary of the qualitative behaviour

LIGHT

d=0

Time (days)

Cell photoadaptation.

Non-chlorophyllian particulate nitrogen pool.

- There is no explicit formulation of the growth rate which is an output of the model.

d=0.3

0

- Chlorophyll a synthesis is enhanced by a decrease of irradiance (red dashed arrow) in order to include the photoadaptation phenomenon.

Photosynthesis

- State variables express total carbon and nitrogen concentrations in chemostat (and not cellular quotas).

d=0

Chlorophyll a (µg.L )

Model hypotheses

Key features:

-1

Table of model parameters

Particulate carbon (µM C)

500

Evolution of chlorophyll a and carbon concentrations at steady state for different dilution rates and two light intensities (solid line: 31 µmol quanta.m-

2.s-1, dashed line: 80 µmol quanta.m-2.s-1). In chemostat cultures, carbon and chlorophyll concentrations (red dots) respectively decrease and increase regularly when the dilution rate is augmented. This kind of constraint strongly inuences the model validation: any model that does not respect such trends can be rejected.

- Bernard O., Malara G. and Sciandra A.,1996. The effects of a controlled uctuating nutrient environment on continuous cultures of phytoplankton monitored by a computer. J. Exp. Mar. Biol. Ecol. 197: 263-278. - Chalup M.S. and Laws E.A., 1990. A test of the assumptions and predictions of recent microalgal growth models with the marine phytoplankter Pavlova lutheri. Limnol. Oceanogr., 35(3): 583-596 - Falkowski P.G and Raven J.A., 1997. Aquatic photosynthesis. Blackwell science. - Flynn K.J., 2001. A mechanistic model for describing dynamic multi-nutrient, light, temperature interactions in phytoplankton. J. Plankton Res., 23(9): 977-997. - Geider R.J., Macintyre H.L. and Kana T.M., 1998. A dynamic regulatory model of phytoplanktonic acclimatation to light, nutrients and temperature. Limnol. Oceanogr., 43(4): 679-694. - Laws E.A. and Bannister T.T., 1980. Nutrient- and light-limited growth of Thalassiosira uviatilis in continuous culture with implications for phytoplankton growth in the ocean. Limnol. Oceanogr., 25(3): 457-473. - Pawlowski L., Bernard O., Le Floc’h E. and Sciandra A., 2002. Qualitative Behaviour of a phytoplankton growth model in photobioreactors. International Federation of Automatic Control,15th IFAC World Congress, Barcelona, Spain, July 21-26,2002. 6p. Accepted - Zonneveld C., 1998. A cell-based model for the chlorophyll a to carbon ratio in phytoplankton. Ecol. Model., 113: 55-70.