Mathematical modelling as a research tool in the ... · Tag der mündlichen Prüfung: 01.06.2017...
Transcript of Mathematical modelling as a research tool in the ... · Tag der mündlichen Prüfung: 01.06.2017...
Mathematical modelling as a research tool in the cyanobacteria
cultivation
Mathematische Modellierung im Mikroalgenanbau
Der Technischen Fakultät
der Friedrich-Alexander-Universität
Erlangen-Nürnberg
zur
Erlangung des Doktorgrades Dr.-Ing
vorgelegt von
Hugo Fabian Lobaton Garcia
aus Palmira, Kolumbien
II
Als Dissertation genehmigt
von der Technischen Fakultät
der Friedrich-Alexander-Universität Erlangen-Nürnberg
Tag der mündlichen Prüfung: 01.06.2017
Vorsitzender des Promotionsorgans: Prof. Dr.-Ing. Reinhard Lerch
Gutachter: Prof. Dr. rer. nat. Rainer Buchholz
Prof. Dr.-Ing. Clemens Posten
III
Acknowledgments
The present work was part of my research activities at the institute of bioprocess engineer in
the University of Erlangen-Nuremberg, headed by Prof. Rainer Buchholz. Special thanks are
dedicated to Prof. Rainer Buchholz for the opportunity to enter in the microalgae world as
well as the helpful discussions about of the practice in microalgae cultivation. Dr.-Ing. Bar-
bara Klein and Dr.-Ing Stephanie Stute are gratefully acknowledged for the initial support
in the laboratory duties. I also thank to Dr.-Ing Holger Hübner and Philipp Schwerma, M.Sc.
for her critical comments on the dissertation.
Thanks to all members of the group of bioprocesses for their valuable contributions through-
out the course of graduate study. Special thanks are also dedicated to the person who helps
me to improve the language in this dissertation and the biggest recognitions go but surely to
my parents who always supported me in this process.
The laws of Nature are but the mathematical thoughts of God. (Euclid)
IV
Abstract
This study will present the development of mathematical model that will be used in a multi-
product strategy for the A. platensis cultivation. Exopolysaccharide with promissory biolog-
ical activities and phycocyanin with interesting properties for the cosmetic and food indus-
tries are the target products. The possible simultaneous production of both high value prod-
ucts with reasonable productivities will be examined. In order to achieve this goal, a mathe-
matical model was developed in three steps. The first one was to model the growth curve for
A. platensis in different culture condition and to test the model fitting performance. Sec-
ondly, the model was used to interpret the results concerning the product formation (phy-
cocyanin and exopolysaccharides). Finally, the model was used to calculate the time and
nitrate concentration additions in order to enhance the co-production of exopolysaccharides
and phycocyanin. The model was tested compared to several culture conditions and it was
able to predict accurately the growth curve of A. platensis after the variations in the flow rate
from 1 to 5 vvm, initial carbon dioxide (0.035 %-3 %) and an incident light intensity on PBR
surface (60-600 µmol m-2 s-1).
Concnerning to product formation, the experimental results show that phycocyanin mass
fraction is degraded as results of the complete nitrate depletion and nitrate additions during
the cultivation help to keep constant this molecule until new macro-element limitation ap-
pear. According to the model, bicarbonate is this limitation. Therefore, a kinetic law for
phycocyanin formation that include this phenome was proposed and linked to the core
model. Regarding the exopolysaccharides formation, this work shows that not only nitrate
depletion is necessary to trigger its formation, as the experiments with nitrate additions
shows better exopolysaccharides production. The exopolysaccharides formation is en-
hanced perhaps as a result of nitrate and other macro-element limitation i.e. phosphate. Fi-
nally, the current work has demonstrated that by controlling nutrient additions such as ni-
trate, reasonable productivities in both products phycocyanin (38 mg l-1 d-1) and exopolysac-
charides (32 mg l-1 d-1) could be obtained.
V
Zusammenfassung
Diese Arbeit stellt die Entwicklung eines mathematischen Modells vor, welches in einer
Multiprozessstrategie für die Kultivierung von A. platensis verwendet wird. Exopolysaccha-
ride, die vielversprechenden biologischen Aktivitäten aufweisen, sowie Phycocyanin, wel-
ches interessanten Eigenschaften für die Kosmetik- und Lebensmittelindustrie besitzt, stehen
dabei als Produkte aus dem Cyanobakterium im Fokus. Dabei wird die gleichzeitige Her-
stellung von den hochwertigen Produkten unter hohen Produktivitätsansprüchen untersucht.
Um dieses Ziel zu erreichen, wurde ein mathematisches Modell in drei Schritten entwickelt.
Zunächst wurde das Wachstums für A. platensis in unterschiedlichen Kulturbedingungen
modelliert und die Modellbefestigungsleistung zu testen. Als nächstes wurde das Modell
verwendet, um die Ergebnisse der Produktkinetiken für Phycocyanin und Exopolysaccharide
zu interpretieren. Schließlich wurde das Modell zur Berechnung der zeitabhängigen Nitrat-
zugaben verwendet, um die Koproduktion von Exopolysacchariden und Phycocyanin zu ver-
bessern.
Das Modell wurde anhand mehrerer Kulturbedingungen getestet und es war in der Lage, die
Wachstumskurve von A. platensis bei Variationen der Durchflussrate von 1 bis 5 vvm, bei
einer CO2-Beimischung von 0,035 % bis 3 % und Lichtintensitäten zwischen 60 und 600
μmol m-2 s-1 genau vorherzusagen.
Die experimentellen Ergebnisse zeigen, dass einerseits die intrazelluläre Phycocyankonzent-
ration sinkt, wenn Nitrat limitierend vorliegt und andererseits dass Nitratzugaben während
der Kultivierung dazu beitragen, die Ausbeute von Phycocyanin konstant zu halten, bis wei-
tere Limitationen auftreten. Gemß dem Modell-Bicarbonat ist diese Beschränkung Bicarbo-
nat. Daher wurde ein kinetisches Gesetz für die Phycocyaninbildung vorgeschlagen und mit
dem Kernmodell verknüpft. Hinsichtlich der Bildung von Exopolysacchariden zeigt diese
Arbeit, dass nicht nur eine Nitratlimitierung notwendig ist, um ihre Bildung auszulösen, da
die Experimente mit Nitratzusätzen eine bessere Produktion von Exopolysacchariden zeigen
Schließlich hat die vorliegende Arbeit gezeigt, dass durch Kontrolle von Nährstoffzusätzen
wie Nitrat Produktivitäten bei beiden Produkten Phycocyanin (38 mg l-1 d-1) und Exopoly-
saccharide (32 mg l-1 d-1) erhalten werden konnten.
Table of contents
Acknowledgments ...................................................................................................... III
Abstract ....................................................................................................................... IV
Zusammenfassung........................................................................................................ V
List of figures ........................................................................................................... VIII
List of tables............................................................................................................... XII
List of abbreviations ............................................................................................... XIII
List of symbols .......................................................................................................... XIV
1 Introduction .................................................................................................. - 7 -
2 State of art ................................................................................................... - 10 -
2.1 The cyanobacteria Arthrospira platensis and its relevance .......................... - 10 -
2.1.1 Phycocyanin: a high value product ............................................................... - 11 -
2.1.2 Phycocyanobilin biosynthetic metabolic pathway ....................................... - 12 -
2.1.3 Exopolysaccharide properties and biosynthesis ........................................... - 16 -
2.2 Mathematical modelling in biotechnology ................................................... - 19 -
2.3 Biomass kinetics models in cyanobacteria ................................................... - 20 -
2.3.1 Genome-scale metabolic models in cyanobacteria ....................................... - 20 -
2.3.2 Macroscale models – Monod type kinetics .................................................. - 21 -
2.3.3 Numerical solutions of the differential equations ......................................... - 22 -
2.3.4 Formation kinetics in biomass and nutrient consumptions .......................... - 23 -
2.3.5 Formation kinetics in product ....................................................................... - 24 -
2.3.6 State of art – Kinetics models in Arthrospira platensis................................ - 25 -
2.4 Modelling photobioreactors features ............................................................ - 26 -
2.4.1 Modelling light supply in photobioreactors.................................................. - 26 -
2.4.2 Mass transfer in photobioreactors ................................................................. - 28 -
2.4.3 Modelling turbulence and light/dark cycles ................................................. - 30 -
3 Project relevance ......................................................................................... - 33 -
4 Proposed mathematical model .................................................................. - 34 -
4.1 Photobioreactor characterization .................................................................. - 35 -
4.1.1 Energy dissipation rate estimation by using CFD ........................................ - 35 -
4.1.2 Light absorption ............................................................................................ - 36 -
4.1.3 Mass transfer coefficient estimation ............................................................. - 36 -
4.2 Macroscale mathematical model .................................................................. - 36 -
5 Materials and methods ............................................................................... - 40 -
VII
5.1 Microalga and media composition ............................................................... - 40 -
5.2 Preculture ...................................................................................................... - 40 -
5.3 Photobioreactor setup ................................................................................... - 40 -
5.4 Analytic determinations ................................................................................ - 42 -
5.4.1 Biomass quantifications and pH measurements ........................................... - 42 -
5.4.2 Nitrate determinations .................................................................................. - 42 -
5.4.3 Phycocyanin determinations ......................................................................... - 42 -
5.4.4 Exopolysaccharides (EPS) quantifications ................................................... - 43 -
5.5 Experimental plan ........................................................................................ - 44 -
6 Results .......................................................................................................... - 45 -
6.1 Photobioreactor computational fluid dynamics characterization: Energy
dissipation rates and liquid velocities ........................................................... - 45 -
6.2 Biomass cultivation results ........................................................................... - 48 -
6.2.1 Gas flow rate experiments and model validation ......................................... - 48 -
6.2.2 Carbon dioxide experiments and model validation ...................................... - 50 -
6.2.3 Light intensity experiments and model validation ....................................... - 53 -
6.3 Product formation results.............................................................................. - 55 -
6.4 Nitrate model validation ............................................................................... - 58 -
6.5 Effects of nitrate on phycocyanin and exopolysaccharides production ....... - 59 -
6.6 Phycocyanin kinetic model ........................................................................... - 62 -
6.7 Literature data simulations ........................................................................... - 63 -
7 Discussion .................................................................................................... - 67 -
7.1 Influence of flow rate on biomass ................................................................ - 67 -
7.2 Influence of carbon dioxide on biomass ....................................................... - 69 -
7.3 Influence of light intensity on biomass and nitrate consumption ................. - 70 -
7.4 Model fitting performance for biomass ........................................................ - 71 -
7.5 Phycocyanin production: biosynthesis, steady state and degradation .......... - 72 -
7.6 Phycocyanin kinetic model ........................................................................... - 75 -
7.7 Exopolysaccharide production ..................................................................... - 76 -
8 Possible experimental errors ..................................................................... - 79 -
9 Model limitations ........................................................................................ - 80 -
10 Final remarks and further study ............................................................... - 81 -
11 Annex ........................................................................................................... - 83 -
12 References .................................................................................................... - 95 -
List of figures
Figure 2-1 A microscope picture from Arthrospira platensis - Cyanobacteria size
around 200 µm with multicellular helical-shaped (Kamata et al. 2014). ..... - 10 -
Figure 2-2 Representation of the light harvesting complex – phycoerythrin (PE),
phycocyanin (PC) and allophycocyanin (APC) together with the Photosystem I
(PSI) and Photosystem II (PSII) (Guan et al. 2007)..................................... - 11 -
Figure 2-3 Molecular structure Phycocyanobilin - Covalently linked to the L-cystein
amino acid to assemble the protein (Brown et al. 1990). ............................. - 13 -
Figure 2-4 Phycocyanobilin and Chlorophyll a pathways beginning from 5-ALA
with relevant Co-factors (Brown et al. 1990)............................................... - 14 -
Figure 2-5 Effect of light intensity on phycocyanin content after 72 hours of
cultivation in the cells of Synechococcus sp. (Takano et al. 1995). ............. - 15 -
Figure 2-6 Insolated Exopolysaccharide from A. platensis (A) and purified EPS –
withe EPS powder isolated by tangential flow filtration followed by freeze
drying (Reichert 2016). ................................................................................ - 17 -
Figure 2-7 A schematic view of key pathways of central metabolism in Arthrospira
platensis - It is supposed that in stress conditions the metabolic pathway is
redirected to glucose-1-phosphate and then to Glycogen or exopolysaccharides
(Cogne et al. 2003). ...................................................................................... - 19 -
Figure 2-8 A schematic representation of the modelling process - one equation may
include a description of how the rate of growth of the biomass depends on the
substrate (Nitrate, light, carbon, etc.) quantities in the photobioreactor, whereas
another equation may include a description of how the substrates are consumed.
- 22 -
Figure 2-9 Particle track at 0.5 m s−1 (top) superposed with a radial light distribution
for two different biomass concentrations of 0.5 and 2 g l−1 (bottom); the light
absorption in the biosuspension was calculated by means of the hyperbolic
model with a light intensity of IO = 150 μE m−2 s−1 at the reactor surface (Perner-
Nochta and Posten 2007). ............................................................................ - 28 -
Figure 2-10 Typical particle trajectories in the draft tube and the split columns - Only
one recirculation is shown for each reactor, while both the front and the top view
of the trajectories are shown respectively in the r–z plane and the cross-sectional
plane. Solid lines inside the figures represent the walls and internals (Luo et al.
2003). - 28 -
Figure 2-11 Gas mass transfer (left) and carbon dioxide in water equilibrium and
carbon uptake at different pH and mechanisms (right) (Markou et al. 2013).- 29
-
Figure 2-12 Schematic of eddies – The higher the energy dissipation rate, the smaller
the eddies size (Sokolichin and Eigenberger 1999). .................................... - 30 -
Figure 4-1 Graphical structure of the mathematical model- The model was divided
in photobioreactor characterization block and cyanobacteria kinetic model
block. - 34 -
Figure 4-2 Bubble column mesh to perform the CFD simulations - 0.05 m diameter
and 0.675 m height. ...................................................................................... - 35 -
Figure 5-1 Photobioreactor screening module (PSM) (Walter et al. 2003). ........ - 41 -
IX
Figure 5-2 Cultivation set up with a gas humidifier in the inlet and cooling system in
the outlet. ...................................................................................................... - 42 -
Figure 5-3 96-well plate with reference and culture supernatant in the different
experiments. ................................................................................................. - 43 -
Figure 6-1 Average energy dissipation rates and average fluid velocities for different
gas flow rates in the photobioreactor. Each data point is an average from all of
the local values in the mesh. ........................................................................ - 45 -
Figure 6-2 Local energy dissipation rates in a front view of the in the photobioreactor
for different gas flow rates (1 vvm and 5 vvm) after 40 s of simulation time. .... -
46 -
Figure 6-3 Local liquid velocities in 1 vvm and 5 vvm in a front view of the in the
photobioreactor for different gas flow rates (1 vvm and 5 vvm) after 40 s of
simulation time. ............................................................................................ - 47 -
Figure 6-4 Simulated and experimental growth of A. platensis in different gas flow
rates. The lines show the results from the simulation of the following conditions:
60 µmol m-2 s-1, 0.035 % carbon dioxide, 30°C, which corresponds to the same
experimental conditions implement in the PSM cultivation. ....................... - 49 -
Figure 6-5 Light attenuation after 100 hours of cultivation in different gas flow rates.
The lines show the results from the simulation of the following conditions: 60
µmol m-2 s-1, 0.035 % carbon dioxide, 30°C, which corresponds to the same
experimental conditions implement in the PSM cultivation. ....................... - 49 -
Figure 6-6 Simulated and experimental pH in different gas flow rates. . The lines
show the results from the simulation of the following conditions: 60 µmol m-2 s-
1, 0.035 % carbon dioxide, 30°C, which corresponds to the same experimental
conditions implement in the PSM cultivation. ............................................. - 50 -
Figure 6-7 Simulated and experimental biomass in 3 % and 0.035 % carbon dioxide
(Top) Simulated and experimental pH at 3 % and 0.035 % carbon dioxide
(Bottom). The lines show the results from the simulation of the following
conditions: 60 µmol m-2 s-1, 1 vvm, 30°C, which corresponds to the same
experimental conditions implement in the PSM cultivation. ....................... - 51 -
Figure 6-8 Simulated and experimental biomass in 3 % and 0.8 % of carbon dioxide
(Top) Simulated and experimental pH at 3 % and 0.8 % carbon dioxide
(Bottom). The lines show the results from the simulation of the following
conditions: 60 µmol m-2 s-1, 1 vvm, 30°C, which corresponds to the same
experimental conditions implement in the PSM cultivation ........................ - 52 -
Figure 6-9 Simulated dissolved carbon dioxide in 3 % and 0.8 % of carbon dioxide.
The lines show the results from the simulation of the following conditions: 60
µmol m-2 s-1, 1 vvm, 30°C, which corresponds to the same experimental
conditions implement in the PSM cultivation. ............................................. - 52 -
Figure 6-10 Simulated and experimental growth at different incident light intensity
on PSM surface. The lines show the results from the simulation of the following
conditions: 1.4 % carbon dioxide, 1 vvm, 30°C, which corresponds to the same
experimental conditions implement in the PSM cultivation. ....................... - 53 -
Figure 6-11 Internal light intensity at different incident light intensity on PSM
surface. The lines show the results from the simulation of the following
conditions: 1.4 % carbon dioxide, 1 vvm, 30°C, which corresponds to the same
experimental conditions implemented in the PSM cultivation. ................... - 54 -
Figure 6-12 Simulated nitrate at different incident light intensity on PSM surface. The
lines show the results from the simulation of the following conditions: 1.4 %
X
carbon dioxide, 1 vvm, 30°C, which corresponds to the same experimental
conditions implement in the PSM cultivation. ............................................. - 55 -
Figure 6-13 Experimental phycocyanin mass fractions at different carbon dioxide
concentrations. Experimental conditions implemented in the PSM cultivation: 1
vvm, 30°C. ................................................................................................... - 56 -
Figure 6-14 Experimental phycocyanin mass fractions at different incident light
intensity on PSM surface. Experimental conditions implemented in the PSM
cultivation: 1.4 % carbon dioxide, 1 vvm, 30°C. ......................................... - 57 -
Figure 6-15 Experimental biomass at different incident light intensity on PSM
surface. (Top) Simulated nitrate at different incident light intensity on PSM
surface. (Bottom). The lines show the results from the simulation of the
following conditions: 1.4 % carbon dioxide, 1 vvm, 30°C, which corresponds to
the same experimental conditions implement in the PSM cultivation ......... - 58 -
Figure 6-16 Experimental and simulated biomass in 600 µmol m-2 s-1 (Top)
Experimental and Simulated nitrate in 600 µmol m-2 s-1 (Bottom). The lines
show the results from the simulation of the following conditions: 1.4 % carbon
dioxide, 1 vvm, 30°C, 0.9 g l-1 initial NO3-, which corresponds to the same
experimental conditions implement in the PSM cultivation. ....................... - 59 -
Figure 6-17 Experimental biomass in control and nitrate Fed batch experiment (Top)
Experimental and simulated nitrate in control and nitrate Fed batch experiment
(Bottom) The lines show the results from the simulation of the following
conditions: 600 µmol m-2 s-1, 1.4 % carbon dioxide, 1 vvm, 30°C, 0.9 g l-1 initial
NO3-, which corresponds to the same experimental conditions implement in the
PSM cultivation. ........................................................................................... - 60 -
Figure 6-18 Phycocyanin mass fractions in control and nitrate fed-batch experiment.
Experimental conditions implemented in the PSM cultivation: 600 µmol m-2 s-
1,1.4 % carbon dioxide, 1 vvm, 30°C, 0.9 g l-1 initial NO3-. ........................ - 61 -
Figure 6-19 Exopolysaccharides mass fractions in control and nitrate fed-batch
experiment. Experimental conditions implemented in the PSM cultivation: 600
µmol m-2 s-1,1.4 % carbon dioxide, 1 vvm, 30°C, 0.9 g l-1 initial NO3- ....... - 62 -
Figure 6-20 Experimental and simulated phycocyanin mass fractions in different
experimental conditions. The lines show the results from the simulation of the
following conditions:,1.4 % carbon dioxide, 1 vvm, 30°C, which corresponds to
the same experimental conditions implement in the PSM cultivation. ........ - 63 -
Figure 6-21 Simulated and experimental biomass from A. platensis (data from
Reichert 2016). The experimental points correspond to cultivation in an open
pond with a diameter of 5 m. The lines show the results from the simulation of
the same experimental conditions applied by Reichert (2016). ................... - 64 -
Figure 6-22 Simulated and experimental biomass from A. platensis (Experimental
data from Jing 2015) (Top) Simulated and experimental nitrate concentrations
(Experimental data from Jing 2015) (Bottom). The lines show the results from
the simulation of the same experimental conditions applied by Jing (2015).- 65
-
Figure 6-23 Simulated and experimental phycocyanin concentration from A.
platensis (Experimental data from Jing 2015). The lines show the results from
the simulation of the same experimental conditions applied by Jing (2015).- 66
-
Figure 7-1 Graphical representation of the medium alkalization mechanism. ..... - 68 -
XI
Figure 7-2 Simulated bicarbonate concentrations in the nitrate fed batch experiment.
The line shows the results from the simulation of the following conditions: 1.4 %
carbon dioxide, 1 vvm, 30°C, which corresponds to the same experimental
conditions implement in the PSM cultivation .............................................. - 76 -
Figure 7-3 Simulated phosphate concentrations in different culture conditions The
lines show the results from the simulation of the following conditions: 1.4 %
carbon dioxide, 1 vvm, 30°C, which corresponds to the same experimental
conditions implement in the PSM cultivation .............................................. - 78 -
XII
List of tables
Table 2-1 Exopolysaccharide production in different light intensities for A. platensis
(Cogne et al. 2003) ....................................................................................... - 18 -
Table 4-1 Summary of parameters and conditions used in the simulation of Arthrospira
platensis ....................................................................................................... - 39 -
Table 5-1 Experimental plan ................................................................................... - 44 -
Table 7-1 Experimental growth rates for different pH in Arthrospira platensis. ... - 70 -
Table 7-2 Final remarks on model fitting performance. ......................................... - 72 -
XIII
List of abbreviations
ALA δ-aminolaevulinic acid
APC Allophycocyanin
CARPT Computer-automated radioactive particle tracking
Ca-Sp Calcium Spirulan
CFD Computational fluid dynamics
DW Biomass dried weight
EPS Exopolysaccharides
GEM Genome scale metabolic
PBPs Phycobilinproteins
PC Phycocyanin
PCB Phycocyanobilin
PE Phycoerythrin
PSM Photobioreactor screening module
PSU Photosynthetic units
vvm Gas volume flow per unit of liquid volume per minute
(volume per volume per minute)
L/D Light and Dark cycles
EPS Exopolysaccharides
XIV
List of symbols
HCO2 Henry’s constant of CO2 (bar l mol-1)
𝐴𝑐𝑠 Cross-sectional area (m2)
𝑀𝐸̅̅̅̅̅ Maintenance without shear effects (h-1)
𝑐𝐶𝑂2 CO2 concentration in gas phase (%)
𝜏𝑐 Critical shear stress (Pascal)
∅ Time fraction in light zone (s)
µmax Maximum specify growth rate (h -1)
B Bicarbonate concentration (g l -1)
bo Initial bicarbonate ion concentration (g l -1)
C Dissolved carbon dioxide (g l -1)
Cp Compensation point (µmol m-2 s-1)
Dp Cyanobacteria diameter (µm)
Ea Scattering coefficient (m2 kg-1of antenna)
Es Absorption coefficient (m2 kg-1 biomass)
I Light intensity (µmol m-2 s-1)
Io Incident light intensity on PBR surface (µmol m-2 s-1)
Kb Monod-half saturation constant of carbon (g l -1)
Ki Monod-half saturation constant of light intensity for bio-
mass (µmol m-2 s-1)
Kip Light inhibition constant (µmol m-2 s-1)
Kla Carbon dioxide volumetric Mass transfer coefficient (h -1)
Kli Monod-half saturation constant of light intensity for phy-
cocyanin kinetic (µmol m-2 s-1)
km Extinction coefficient for shear stress (Pascal-1)
Kn Monod-half saturation constant of nitrate (g l -1)
Kpc Monod-half saturation constant of phycocyanin (g gbio-
mass-1)
N Nitrate concentration (g l -1)
no Initial nitrate concentration (g l -1)
P Gas inlet absolute pressure (bar)
P Phosphate (g l -1)
Pc Phycocyanin concentration (g l -1)
Pk Acid dissociation constant
Po Initial phosphate concentration (g l -1)
Q Volumetric flow rate (l h-1)
R Bubble column radius (m)
Rpc Phycocyanin formation rate (h -1)
V Dissolved carbon dioxide concentration (g l -1)
Vs Superficial gas velocity (m s-2)
X Total biomass concentration (g l -1)
Xa Active biomass concentration (g l -1)
xao Initial biomass (g l -1)
yb/x Bicarbonate consumption yield (g gbiomass-1)
yn/x Nitrate consumption yield (g gbiomass-1)
yp/x Phosphate consumption yield (g gbiomass-1)
Zpc Mass fraction of phycocyanin (gphycocyanin gbiomass-1)
𝑓 Light/dark frequencies (Hz)
𝜀 Energy dissipation rate (m2 s-3)
VIII
𝜆 Eddy length (µm)
𝜇𝑙 Fluid viscosity (Pascal×s)
𝜌𝑙 Fluid density (kg m-3)
𝜏 Shear stress (Pascal)
- 7 -
1 Introduction
The cyanobacterium Arthrospira platensis is a prokaryotic photoautotrophic microorganism
that is successfully cultivated for the commercialization as whole biomass due to its high pro-
tein content and promising valuable substance. For instance, phycocyanin ─ a light harvesting
protein present in A. platensis ─ has recently drawn the interest of the food and cosmetic indus-
tries due to its bright blue colour and its strong antioxidant capacities. Additionally, other po-
tential compounds, which are present in A. platensis are gama-linoleic acid ─ an essential un-
saturated fatty-acid and Calcium-Spirulan ─ a sulphated exopolysaccharide with promissory
biological activities (Borowitzka 2013; König 2007; Pulz and Gross 2004). Although A. platen-
sis is successfully cultivated in open raceways, the low productivities of biomass dried weight
(DW) reached in these cultivations (0.04 g DW l-1 d-1) (Jiménez et al. 2003) and the unreliable
product quality (i.e phycocyanin) seem to require the cultivation of this cyanobacteria in pho-
tobioreactors.
Biomass productivities up to 20 times higher than those reached in raceway cultivations
(Bezerra et al. 2011; Chen et al. 2013) have been found by using closed photobioreactor sys-
tems. Although growth is relevant in cyanobacteria production, as in many other biotechnolog-
ical processes, the product formation is the main goal. Therefore, to become economically fea-
sible, the cultivation of cyanobacteria in photobioreactors requires optimal product yields cou-
pled with low plant investment and operating costs (Bertucco et al. 2014). Optimal strategies
for nutrient delivery, as well as the accurate use of light, are the key parameters that could make
this technology promising in order to achieve higher efficiencies. In addition, the efficiency of
the process can be enhanced with a multiproduct strategy already proposed for cyanobacteria,
which implies the recovery of more than one useful compound.
A. platensis use phycocyanin as a light-harvesting protein and consequently, light intensity and
nitrate are crucial factors in the accumulation of this phycobiliprotein (Chen et al. 2013). How-
ever, the values of optimal nitrate and light intensity for phycocyanin production found in re-
search papers are inconsistent, possibly due to different bioreactor configurations and culture
conditions (Xie et al. 2015). For instance, (Chen et al. 2013) reported that the maximal phy-
cocyanin productivity (125 mg l-1 d-1) of A. platensis was obtained at 700 µmol m-2 s-1. In con-
trast to this, Xie et al stated inhibition in growth by using the same light intensity (Xie et al.
2015). The discrepancy in these results can be explained by dissimilar light paths, diverse light
- 8 -
qualities or different initial cell densities used in both cases (0.5 g l-1 (Chen et al. 2013) In
addition, in batch cultivation, nutrients like nitrate, carbon and light decrease with the time and
therefore, the cyanobacteria composition (phycocyanin, exopolysaccharides protein and lipids)
also suffered quantitative and qualitative changes. Therefore, a mathematical model can facili-
tate the investigation of the optimal conditions according to particular cultivation settings.
A. platensis – when cultivated under photosynthetic growth conditions − produces different
quantities of an associated exopolysaccharide (EPS) depending on experimental parameters
(Borowitzka 2013; Pulz and Gross 2004). According to Filali et al, the exopolysaccharide sugar
composition consists of 6 neutral sugars − xylose, rhamose, fructose, galactose, mannose, glu-
cose; 2 uronic acids − glucuronic and galacturonic acid; 2 unidentified sugars, as well as some
sulphate groups, whose localization is still not completely clear (Filali Mouhim et al. 1993).
The possibility of stimulating polysaccharide release by means of an optimization of the culture
conditions has been poorly considered.
The primary source of inorganic carbon for A. platensis is the bicarbonate ion (HCO3-) (Cornet
et al. 1998). The bicarbonate present in the medium (around 117 mM) is consumed by the cya-
nobacteria to support its growth. With the purpose of avoiding carbon limitations and taking
advantage of the carbon dioxide captures, A. platensis cultures may be provided with additional
CO2. In addition, in microalgal culture technics, carbon dioxide is also used to control the pH
(Pawlowski et al. 2014). A carbon dioxide line is opened or closed automatically according to
an established pH set point. This control technique has provided promising performance results
with an adequate reduction of the CO2 losses (Pawlowski et al. 2014). However, this implies
the necessity of sensors in the reactor to measure these variables, which can increase investment
and operating costs. A predictive CO2 supply based on a mathematical model can ease the re-
search activities and overtake the already mentioned challenge.
Mathematical models are valuable tools to investigate and optimize bioprocess (Fleck-
Schneider et al. 2007). Therefore, several attempts have been conducted to simulate A. platensis
growth (Cornet et al. 1992; Levert and Xia 2001). Nonetheless, all of them have been applied
just for low cell densities (< 1g l-1) and they have neglected carbon limitations in culture. In
addition, phycocyanin and exopolysaccharide formation laws have not been deeply docu-
mented.
- 9 -
The aim of this study is to extend these models to higher biomass conditions of A. platensis in
bubble columns. The model will be used also to investigate the phycocyanin and exopolysac-
charide formation under different scenarios and the proof of concept of controlling nutrients for
optimal product formation.
- 10 -
2 State of art
The theoretical part of this thesis will firstly describe the cyanobacteria Arthrospira platensis
together with its compounds phycocyanin and exopolysaccharides, as well as their relevance
within various industries. Furthermore, the importance of mathematical models and simulations
in biotechnological processes will be explained and then applied on this particular group of
cyanobacteria. Not last, various aspects like the light supply, mass transfer and turbulence will
be considered within this chapter.
2.1 The cyanobacteria Arthrospira platensis and its relevance
Arthrospira sp. are filamentous prokaryote cyanobacteria with at least 38 species already de-
scribed in the literature. The most representative strains in the industry are Arthrospira platensis
and Arthrospira maxima. A. platensis is a multicellular helical-shaped alga and the morpholog-
ical features are highly dependent on the parameters of cultivation. The literature describes a
big range of lengths and spirals: from 200 µm with 6 spirals to 1150 µm with 12 spirals (Figure
2-1). This size range depends on the culture environments. For example, nitrogen limited cul-
tures seem to have a long shape due to the glycogen accumulation. However, even if the cells
are extending their shape, there is no evidence of cell division (Cornet et al. 1998)
Figure 2-1 A microscope picture from Arthrospira platensis - Cyanobacteria size around 200 µm
with multicellular helical-shaped (Kamata et al. 2014).
The quantity of carbohydrates in dried A. platensis powder represents around 10 to 20 % of the
total algae mass. These carbohydrates can be found in both intracellular and extracellular envi-
ronment, while the percentage of lipids varies between 6 to 10 %. Gamma-linolenic acid, a fatty
- 11 -
acid sold as a dietary supplement, represents almost 30 % of A. platensis lipids (Cornet et al.
1998). The high concentration of proteins in A. platensis is an advantage and it is one of the
reasons why the World Health Organization indicates this alga as a healthy food. The percent-
age of proteins varies between 59 to 71 % in dry weight depending on the culture conditions.
Instead of chloroplast, A. platensis have special structures called phycobilisomes (Cornet et al.
1998) which are localized in the thylakoid membrane (Figure 2-2). These granules contain phy-
coerythrin (PE), phycocyanin (PC) and allophycocyanin (APC), which are important phyco-
bilinproteins (PBPs) in the photosynthesis process together with chlorophyll A.
Figure 2-2 Representation of the light harvesting complex – phycoerythrin (PE), phycocyanin (PC)
and allophycocyanin (APC) together with the Photosystem I (PSI) and Photosystem II
(PSII) (Guan et al. 2007).
2.1.1 Phycocyanin: a high value product
The phycocyanin (PC) is the main protein-pigment with the highest quantity in A. platensis
(4 % to 20 %) (Chen et al. 2013; Xie et al. 2015). The major industrial applications of phycocy-
anin protein are related to its antioxidant capacity and to its bright blue which makes it a poten-
tial pigment for food and cosmetic industry. The purity of phycocyanin is measured by the
absorbance ratio A620/A280 with the purity values of 0.7 and 4.58 depending on food grade and
analytic grade. The blue chromophore group in phycocyanin is the Phycocyanobilin molecule
(Figure 2-3). It is covalently linked to the L-cystein amino acid. Phycocyanobilin biosynthesis
will be described afterwards in more detail.
It is important to highlight that the maximum phycocyanin productivity (840 mg l-1 d-1) was
achieved with the cultivation of Galdieria sulphuraria in heterotrophic conditions. To achieve
this, a high rate of biomass production at high biomass concentration (83.3 DW g L-1) together
with a strain that has relatively a high specific phycocyanin concentration (15.6 mg g-1)
- 12 -
(Querques et al. 2015) were produced in continuous culture mode. This serious drawback of
photosynthetic microorganisms compared to heterotrophic cultivations could be partially dis-
regarded in view of some advantages, of both environmental and economic impact, that photo-
autotrophic cultivations could achieve : (i) they are capable of utilising energy from the sunlight
instead of glucose; (ii) many strains can grow in brackish or in waste waters ; (iii) it is possible
to utilise as carbon source the CO2 emitted by industrial plants ; (iv) the economy of the process
could be enhanced by recovering more than one useful compound, with a multiproduct strategy
as already proposed for cyanobacteria
The phycobilinproteins (PBPs), in particular phycocyanin, have been widely used as nutritional
ingredients, natural dyes and florescent markers for pharmaceuticals such as antioxidants and
anti-inflammatory reagents (Querques et al. 2015). The phycobilinproteins serve as valuable
fluorescent tags with numerous applications in flow cytometry, fluorescence and activated cell
sorting. These applications exploit the unique physical and spectroscopic properties of phyco-
bilinproteins. In addition, because of the high molecular absorptivity of these proteins at visible
wavelengths, they are convenient markers in applications like gel electrophoresis, isoelectric
focusing and gel exclusion chromatography (Querques et al. 2015).
Phycocyanin is used also as colorant in food (chewing gums, dairy products, jelly, etc.) and in
cosmetics such as lipstick and eye liners in Japan, Thailand and China. Phycocyanin is one of
the most important natural blue pigment used in food and biotechnology because of its color,
fluorescence and antioxidant properties with estimated marker is around 5 to 10 million of dol-
lar yearly and growing (Querques et al. 2015).
The extraction of phycobilinproteins involves cell rupture and release of these proteins from
the inside of the cell. Several methods have been developed for the separation and purification
of PC, such as density gradient centrifugation, ammonium sulfate precipitation, chromatog-
raphy method and aqueous two phase extraction. One of the most difficult steps in the extraction
of phycobilinproteins is the wall cell break. Thus, the use of variations in the osmotic pressure,
abrasive conditions, chemical treatment, freezing-thawing, sonification and tissuelyser are nec-
essary (Kumar et al. 2014). Mechanically cell disintegration methods are currently preferred
for large-scale operations.
2.1.2 Phycocyanobilin biosynthetic metabolic pathway
The Phycocyanobilin (Figure 2-3) is the blue chromophore in the phycocyanin molecule and it
shares common biosynthetic pathways with heme and chlorophyll to the level of protoporphyrin
- 13 -
IX. Both are assembled from δ-aminolaevulinic acid (ALA), which is synthesized from gluta-
mate via the C5 pathway, whereas the pathways diverge upon metalation with either iron or
magnesium (Figure 2-4). In the later stages of phycocyanobilin synthesis, the protoheme is bro-
ken down to bilieverdin. And finally, cyanobacteria possess ferredoxin-dependent bilin reduc-
tases primarily for the synthesis of Phycocyanobilin from bilieverdin (Brown et al. 1990)
Figure 2-3 Molecular structure Phycocyanobilin - Covalently linked to the L-cystein amino acid to
assemble the protein (Brown et al. 1990).
Next, the effect of light conditions and nitrate concentrations in the biosynthesis of this mole-
cule will be addressed.
2.1.2.1 Light
The light harvesting protein that belongs to the photosynthetic units, together with the mass
fractions phycocyanin and its chromophore group are regulated by light. According to Rubio
cells are known to adapt their number and size of photosynthetic units (PSUs) or phycobili-
somes to the available irradiance when this is constant for a prolonged period (Rubio et al.
2003). This phenomenon is also known as photoadaptation. Moreover, the cells that are accli-
mated to high irradiance have fewer PSUs and contain less chlorophyll and phycocyanin than
the same type of cells that are growing under low irradiance (Rubio et al. 2003). In contrast to
this, the concentration of PSUs in the cell increases under low irradiance. It is important to
highlight that all PSUs reach their steady-state value in hours, either from a culture transfer
from low light to high light or vice versa (Ritz et al. 2000).
5- ALA
Light induction
- 14 -
PORPHOBILINOGEN
UROPORPHYRINOGEN III
COPROPORPHYRINOGEN III
PROTOPORPHYRINOGEN IX
PROTOPRPHYRIN IX
CHLOROPHYLL a PROTOHEME IX α
PHYCOCYANOBILIN
Figure 2-4 Phycocyanobilin and Chlorophyll a pathways beginning from 5-ALA with relevant Co-
factors (Brown et al. 1990).
This photoadaptation process has been found not only in all light harvesting chlorophylls, phy-
coerythrin and phycocyanin, but also within all light harvesting carotenoids like fucoxantin and
peridinin (Dubinsky and Stambler 2009). For example, the effect of light intensity on phycocy-
anin content in the cyanobacterium Synechococcus sp. was addressed by (Takano et al. 1995).,
who found a maximum of phycocyanin production at 25 µmol m-2 s-1 (Figure 2-5), whereas
light intensities above or below this value decrease the phycocyanin content. Additional studies
have shown that a light increment above the optimal level leads to a reduction in the expression
of phycocyanobilin structural genes (Lau et al. 1977), fact that can be related to the photoadap-
tation process.
- 15 -
Figure 2-5 Effect of light intensity on phycocyanin content after 72 hours of cultivation in the cells
of Synechococcus sp. (Takano et al. 1995).
2.1.2.2 Nitrate
The main nitrogen source of A. platensis is the nitrate (NO3-) ion which is 29 mM in the standard
spirulina medium. Nitrate is carried through membrane by active transport and then reduced to
ammonium (NH4+) (equations below), after which it is incorporated into glutamic acid in the
amino acid metabolism. The proportion of the reducing power that needs to be used for nitrogen
assimilation can be reduced to 10 % of the total by assimilating ammonium. It is reasonable for
cyanobacteria to show a strong preference for ammonium (NH4+) over nitrate (NO3
-), whereas
the use of ammonia salts, mainly NH4Cl and (NH4)2SO4, has been reported. However, they
cannot replace the total amount of nitrate because high quantities of ammonia seem to be toxic
(Converti et al. 2006).
NO3- + 2 reduced-ferredoxin + 2 H+ => NO2
- + 2 oxidized-ferredoxin + H2O
NO2- + 6 reduced-ferredoxin + 7 H+ => NH4
+ + 6 oxidized-ferredoxin + 2 H2O
Furthermore, it has been found that under complete nitrate deprivations, phycocyanin is de-
graded in some cyanobacterium species (Gilbert et al. 1996; Lau et al. 1977). A study made in
Synechococcus sp shows the loss of spectrophotometrically measurable phycocyanin after the
resuspension in nitrate-free medium. Once the nitrate was restored, phycocyanin was resynthe-
sized and its content began to increase (Takano et al. 1995). However, low but non-limiting
- 16 -
nitrate conditions have been also found positive for the biosynthesis of phycocyanin. Moreover,
(Xie et al. 2013) found a better lutein formation by maintaining the nitrate concentration below
2.2 mM without reaching complete depletion.
2.1.3 Exopolysaccharide properties and biosynthesis
A. platensis is cultivated under photosynthetic growth conditions and produces different quan-
tities of an associated exopolysaccharide (Figure 2-6) depending on the culture conditions
(König 2007; Pulz and Gross 2004). According to the early literature the exopolysaccharide
sugars composition consists of 6 neutral sugars, xylose, rhamnose, fructose, galactose, man-
nose, glucose, 2 uronic acids: glucuronic and galacturonic acid and 2 unidentified sugars and
the presence of sulphated groups, whose localization is still not completely clear. Uronic acids
were found to contribute to 40 %. (Filali Mouhim et al. 1993). Another study it has been re-
ported that cyanobacterial EPS are not only composed of carbohydrates but also of other mac-
romolecules such as polypeptides enriched with glycine, alanine, valine, leucine, isoleucine and
phenylalanine have been reported in the EPS. Recently, a partial EPS characterization indicated
by using elemental analysis and a bicinchoninic acid (BCA) reaction that the EPS were hetero-
polysaccharides that contain carbohydrate (13%) and protein (55 %) moieties. In addition, gas
chromatography analysis of the carbohydrate portion of the EPS indicated that it was composed
of seven neutral sugars: galactose (14.9 %), xylose (14.3 %), glucose (13.2 %), fructose
(13.2 %), rhamnose (3.7%), arabinose (1%), mannose (0.3%) and two uronic acids: galac-
turonic acid (13.5 %) and glucuronic acid (0.9 %)(Trabelsi et al. 2009).
However, an additional study shows 57 % protein and 43 % carbohydrates with the following
sugar composition: galactose (4.3 %), xylose (6.2 %), glucose (17.3 %), frucose (15.2 %), rham-
nose (49 %), mety-rhamose (17 %), mannose (2.3 %) and glucuronic acid (3.95 %) (König
2007).
- 17 -
Figure 2-6 Insolated Exopolysaccharide from A. platensis (A) and purified EPS – withe EPS powder
isolated by tangential flow filtration followed by freeze drying (Reichert 2016).
The differences found in the sugar composition can be explained by the fraction of the extract
where the monosaccharides were analysed. For example, an study analysed the sugar composi-
tion from the EPS in the supernatant (culture medium) and also in an extract that contains the
EPS from the external layers of cells and they found a difference in the molar rations of the
monosaccharide composition between the both fractions (König 2007; Nie et al. 2002; Xia et
al. 2001).
Many studies have reported that the exopolysaccharides from A. platensis have a particular
variety of biological applications including antiviral, inhibitory effects on corneal neovascular-
ization and booster of the immune system (Chaiklahan et al. 2013). Calcium Spirulan (Ca-Sp)
(Hayashi et al. 1996) is a sulphated exopolysaccharide (17.7 mg g-1 exopolysaccharides) that
was found to inhibit the replication of several enveloped viruses, including Herpes simplex
virus type, human cytomegalovirus, measles virus, influenza A virus and HIV-1 virus. It was
also revealed that Ca-Sp selectively inhibited the penetration of the virus into host cells with a
high relevance for the antiviral activity of the sulphated groups and for the molecular confor-
mation by chelation calcium ion with sulfated groups). Ca-Sp is also particularly interesting for
its use in cosmeceuticals. It stimulates the metabolic activity of human skin fibroblast cell lines,
which are responsible for collagen synthesis and for the firmness of skin (Pulz and Sandau
2009). With increasing age, the collagen synthesis drops significantly, so a main target in the
cosmetic research is the development of anti-aging products that are capable of enhancing the
metabolism of fibroblast. A 36% enhancement of collagen synthesis was found by applying
CA-Sp at 10 µg ml -1. It was also found that UV exposed fibroblasts showed a higher vitality,
if Ca-Sp had been added prior to or even after radiation (Pulz and Sandau 2009).
- 18 -
In addition, the exopolysaccharides show non-Newtonian behavior and strong pseudo-plastic
characteristics at a concentration of 0.02 g EPS l-1 and therefore, due to its rheological charac-
teristics, EPS from A. platensis has been proposed as possible substitute for agar-agar study
shows an increment in the medium relative viscosity with the increment of the EPS in medium
(Filali Mouhim et al. 1993). This increment can also generate additional challenges in A. platen-
sis production and scale-up.
Under unfavorable growing conditions many algae shift their metabolic pathways toward the
biosynthesis of exopolysaccharides. In batch cultivations, this can occur during the course of
the cultivation as a result of the changes in substrates like light, nitrate, phosphate and carbon.
However, the possibility of stimulating polysaccharide release by means of an optimization of
the culture conditions has been poorly considered. A research studied the light influence in the
exopolysaccharides formation. Table 2-1 shows the values of exopolysaccharides in different
light conditions. Incident light intensity on PBR surface up to 1000 µmol m-2 s-1 favor the pro-
duction of exopolysaccharides by reaching a maximum of 0.54 g polysaccharides g-1 biomass.
It has been identified that exopolysaccharides can be delivered as result of an overflow in the
metabolism (Staats et al. 2000), which generates a drain the excess of ATP (Cogne et al. 2003)
by them. Similar to phycocyanin production, low, but not growth limiting, concentrations of
nitrate have demonstrated to enhance the accumulation of exopolysaccharide (Staats et al.
2000). For example, (Abd El Baky et al. 2014) found the best exopolysaccharide production at
nitrate concentrations between 0.2 g L-1 to 0.5 g L-1 nitrate, whereas the highest values of growth
were found in concentrations of 1.8 g L-1 of nitrate. Analyzing the general metabolism for A.
platensis (Figure 2-7) proposed by (Cogne et al. 2003). It is supposed that in stress conditions
the metabolic pathway is redirected to glucose-1-phosphate and then to Glycogen or exopoly-
saccharides. Excess of energy in form of ATP may lead the exopolysaccharide production.
Table 2-1 Exopolysaccharide production in different light intensities for A. platensis (Cogne et al.
2003)
Irradiance
(µmol m-2 s-1)
Exopolysaccharide
(g polysaccharides g-1 biomass)
92 0.1
228 0.33
731 0.50
1000 0.54
- 19 -
Figure 2-7 A schematic view of key pathways of central metabolism in Arthrospira platensis - It is
supposed that in stress conditions the metabolic pathway is redirected to glucose-1-phos-
phate and then to Glycogen or exopolysaccharides (Cogne et al. 2003).
2.2 Mathematical modelling in biotechnology
Mathematical models are valuable tools to predict and understand the behavior of biological
systems. In addition, they can be used to describe the past performance and predict the future
performance of biotechnological processes. They can be applied to processes operating at many
different levels, from the action of an enzyme within a cell, to the growth of that cell within a
commercial scale bioreactor (Nielsen et al. 1991).
The majority of the goals of modeling cell factories are related to understanding and predicting
their behavior when they are perturbed either internally through genetic modifications, or ex-
ternally by changing various environmental factors. The model purpose defines the complexity
of the modeling problem and will influence all subsequent steps of the modeling procedure
(Nielsen et al. 1991).
- 20 -
Mathematical models can be powerful tools in both fundamental research and applied research
and development. Some models contribute to the understanding of how cells function, while
other models allow us to use laboratory and pilot-scale data to make predictions about how a
commercial scale bioreactor must be designed and operated in order to give optimal perfor-
mance. For example, mathematical models have been widely used within classical fermenta-
tion, glucose fed-batch strategies to enhance ethanol production or the microbiological L-leu-
cine production (Georgiev et al. 1997). Other biotechnological products which have benefited
from mathematical modelling and simulation of fermentations are: citric acid (Zlateva et al.
1993) and penicillin-G (Menezes et al. 1994).
Furthermore, many different types of biotechnological systems and processes, such as the op-
eration of metabolic pathways within a cell, the expression of genes within a cell, the death of
cells during a sterilization process, the growth of cells in a bioreactor and the action of enzymes
can be modeled (Nielsen et al. 1991). Nonetheless, in the field of cyanobacteria biotechnology,
few mathematical models have been developed to simulate cyanobacteria growth with less or
more details depending on the purpose for which the model was built. The level of accuracy in
the kinetic equations varies from the classical Monod approaches to more sophisticated genome
scale models and they will be described in the next section
2.3 Biomass kinetics models in cyanobacteria
In the following theoretical part, the advantages and the current limitations of the modern ge-
nome scale models are described, as well as the classical macroscale modelling base on differ-
ential equations couple with production or/and consumption kinetics for cyanobacteria cultiva-
tions. In addition, a short description of the numerical approaches to solve the models is given.
Finally, the general approaches for biomass and product formation in microalgal culture are
addressed.
2.3.1 Genome-scale metabolic models in cyanobacteria
In modern, system-level microbial metabolic engineering, genome scale metabolic reconstruc-
tions (GEMs) are used to integrate and analyze large omics datasets as well as to evaluate de-
signs in silico. A GEM maps annotated metabolic genes and proteins to reactions based on the
current best understanding of a given organism. A growing number of metabolic engineering
studies in classical microbial strains have demonstrated the use of well-curated GEMs to gen-
erate strain designs that are neither intuitive nor obvious (Baart and Martens 2012).
- 21 -
However, currently there are a few genome scale reconstructions available for cyanobacteria.
For example, the metabolic network of the cyanobacterium Synechocystis sp. has been deeply
addressed by various research groups in the world. More recently quasi-steady state simulations
of the A. platensis metabolic network have been done. A simpler metabolic network was built
up with 121 reactions and 134 metabolites including biomass synthesis, production of a growth
associated polysaccharide and energy aspects (Cogne et al. 2003).. Another more sophisticated
metabolic network of A. platensis was generated by (Klanchui et al. 2012), which accounts for
771 metabolic genes, 712 metabolites and 868 reactions More than 85 % of the total reactions
were associated with genes. The simulated results were validated by experimental evidence and
showed satisfactory agreement under three different growth conditions: autotrophic, hetero-
trophic, and mixotrophic.
Genome-scale models are able to estimate the flux distribution of the entire metabolism. How-
ever, they are still immature due to the lack of information in most of microalgal species over
all cellular biochemical reactions. In addition, most of the studies have focused only on the
quasi-steady state under constant light and nutrient regimes. Static metabolic studies can give
a first insight in the behavior of continuous cultivations, but until now they couldn’t be success-
fully implemented in batch or fed-batch cultivations due to changes in the culture conditions
over the time, which probably implies higher computational resources (Baart and Martens 2012;
Baroukh et al. 2015)
2.3.2 Macroscale models – Monod type kinetics
Macroscale models are based on differential equations and simple consumption or formation
kinetic terms. As it was already mentioned they have been widely used in classical fermenta-
tions. Differential equations describe, in a simplified manner, how the key physical and bio-
logical phenomena operate. Figure 2-8 shows a simplified illustration of how a model that con-
sists of differential equations might be applied to a cyanobacteria process.
As Figure 2-8 displays, one equation may include a description of how the rate of growth of the
biomass depends on the substrate (Nitrate, light, carbon, etc.) quantities in the photobioreactor,
whereas another equation may include a description of how the substrates are consumed. These
equations describe the rate of change in biomass, substrates and products but not the actual
value of these variables. Therefore, these equations need to be solved and under some condi-
tions these differential equations can be either analytically integrated or simplified in order to
give algebraic equations, but this is very often not the case and a numerical solution is required.
- 22 -
Figure 2-8 A schematic representation of the modelling process - one equation may include a de-
scription of how the rate of growth of the biomass depends on the substrate (Nitrate, light,
carbon, etc.) quantities in the photobioreactor, whereas another equation may include a
description of how the substrates are consumed.
2.3.3 Numerical solutions of the differential equations
Runge-Kutta methods are iterative techniques, which are used in temporal discretization for the
approximation of solutions for ordinary differential equations. The Runge-Kutta algorithm lets
us solve a differential equation numerically (i.e. approximately) and it is known to be very
accurate and well-behaved for a wide range of problems.
Consider the single variable problem: dx
dt= f(t, x) with initial condition x(0) = x0. Suppose that
xn is the value of the variable at time tn. The Runge-Kutta formula takes xn and tn and calculates
an approximation for xn+1 at a brief time later, tn+h. It uses a weighted average of approximated
values of f (t, x) at several times within the interval (tn, tn+h). The formula is given as it follows:
Equation 1: xn+1 = xn +h
6× (a + 2b + 2c + d)
Equation 2: a = f(tn,, xn)
Equation 3: b = f (tn +h
2, xn +
h
2× a)
Equation 4: c = f (tn +h
2, xn +
h
2× b)
Equation 5: d = f(tn + h, xn + h × c)
- 23 -
To run the simulation, we start with x0 and find x1 using the formula above. Then we plug in
x1 to find x2 and so on. The Runge-Kutta method is included in Matlab thought a routine called
ODE45, which was used in this work to solve the differential equations set.
2.3.4 Formation kinetics in biomass and nutrient consumptions
The right side in the biomass differential equation, i.e (Equation 6); can be set with simple mac-
roscopic kinetic laws that relates growth rate to extracellular concentration in limiting substrates
(i.e. light, nitrate, etc.) These laws are established mainly with Monod model, where Ki is the
substrate concentration that reduces the maximum growth rate to the half.
Equation 6: 𝑑𝑥
𝑑𝑡= µ𝑚𝑎𝑥 ×
𝐼
𝐼+𝐾𝑖×
𝑓1
𝑓1+𝐾𝑓1×
𝑓1+𝑛
𝑓1+𝑛+𝐾𝑓1+𝑛
Equation 7: 𝑑𝑓1
𝑑𝑡= −𝑌𝑓1
𝑥
×𝑑𝑥
𝑑𝑡
Although several limiting factors can be added to the Equation 6, the main drawback in formu-
lating general kinetic laws in limiting conditions is to find simple macroscopic laws that relate
growth rate to extracellular concentration in limiting substrates (Bungay 1994). This requires
not only a complete understanding of the mechanisms involved in the limiting process, but also
to study them at different levels (metabolism, physiology, etc) (Lee et al. 2015) In the case of
photosynthetic micro-organisms, these mechanisms become more complex because two or
more limiting factors interact, since these micro-organisms are always cultivated in limited light
conditions (Lee et al. 2015).
Currently, the main variation in the model presented above consists in how the effect of light
on the growth rate is modeled 𝐼
𝐼+𝐾𝑖. Simple models do not include the photo inhibition and photo
adaptation processes in cells (Merchuk and Wu 2003) and they are directly related to the max-
imum specific growth rate as the Equation 6 states. More sophisticated kinetic models include
photo inhibition and photo adaptation processes in cells such as the one proposed by Eilers and
Peeters and advance by Wu and Merchuk (Eilers and Peeters 1988; Wu and Merchuk 2002)
who describe the relationship between growth and biomass with four equations instead of one.
This approach has been successfully used by Al-Dahhan (Luo and Al-Dahhan 2004) and other
authors in their simulations of the red marine cyanobacteria Porphyridium sp.
The Eilers and Peeters model assumes that the PSU (photosynthetic units) has three stages: the
resting stages x1, the activated state x2 and the inhibited state x3. The probabilities of the state
transitions following a photon capture are supposed to be proportional to the light intensity, or
these reactions are assumed to be first- order reactions with reaction constants of 𝛼I for x1→x2
- 24 -
and βI for x2→x3. Since the other-state transitions can happen in the dark, the reaction constants
for these reactions are assumed to be constant, i.e. δ for x2→x1 and γ for x3→x2. Nonetheless,
the model needs a lot of empirical parameters and its use with other cyanobacteria are very
scarce in the literature, which limits the application on other species. (Eilers and Peeters 1988).
All nutrient consumptions can be correlated with theoretical consumptions yields (Equation 7),
which are calculated from Stoichiometric equations and the biomass formation rate dx
dt. In ad-
dition, light also has to be supplied in each time step. However, this “nutrient” is more chal-
lenging to model because light varies with time and also in the space as consequence of the
biomass growth. Further in this work, it will be explained how light (I) is model by taking into
account the light absorption and scattering properties by the cyanobacteria.
2.3.5 Formation kinetics in product
The biomass composition in the cells changes with the time. However, most of the available
mathematical models for bioprocesses are unstructured. This means that the biomass is consid-
ered as one entity and is described only by its concentration, whereas product formation is
linked to the biomass formation by linear relations (Equation 8) (Nielsen et al. 1991). In other
words the product mass fraction Zp is constant during the cultivation; however this assumption
is not completely correct.
Equation 8: 𝑑𝑝
𝑑𝑡= 𝑍𝑝 ×
𝑑𝑥
𝑑𝑡
Advanced structured models consider that the biomass can change its composition during the
time of cultivation as a result of the changes in substrates. Especially the Zp is not constant and
it should change as consequence of the metabolic pathway shifting. Structured models describe
not only the biomass kinetics, but also in particular the product formation kinetics for transient
operation, using a small set of parameters which often have a biological meaning. Therefore,
product mass fractions have to be modeled by introducing a simple macroscopic law that links
the biological phenomena in the cell with the biosynthesis and degradation of product during
the batch cultivation. Consequently, a new differential equation for phycocyanin mass fraction
dZp
dt that describes its changes during the time is necessary:
Equation 9: 𝑑𝑝
𝑑𝑡= 𝑍𝑝 ×
𝑑𝑥
𝑑𝑡
Equation 10: 𝑑𝑍𝑝
𝑑𝑡=?
- 25 -
The challenge is to describe in a suitable manner the right term in the Equation 10 because of
the lack of information about the mechanisms that trigger biosynthesis and degradation of the
cyanobacteria components, particularly phycocyanin and exopolysaccharides. At first glance,
microorganisms appear to be very different, but a closer study reveals that they have a number
of basic functions in common. For example, they all need catabolism of substrate to create
energy for growth and maintenance of cell functionality
In microalgae modelling, the number of studies that have included the kinetic of product for-
mation is very scared and limited to low cell densities. A study includes in their model a mech-
anism to describe the phycoerythrin formation. Their mathematical model was well suited to
understand the complex variations in the biomass composition for low cell densities cultivations
of Porphyridium purpureum (Csőgör et al. 2001; Fleck-Schneider et al. 2007). In the case of A.
platensis, a model proposed by (Levert and Xia 2001) incorporates the exopolysaccharide for-
mation mechanism (Levert and Xia 2001). However, the model was validated just in low light
conditions that produce low cell densities (1g l-1). It limits the model extrapolation to other
conditions, such as in the case of using high light intensity (>100 µmol m-2 s-1).
To sum up, the product formation is the goal in many biotechnological processes, so that the
kinetics of product formation can be more relevant than the kinetics of growth. Therefore, it is
necessary to understand the interrelations between the cultivation conditions and the product
formation and to implement these in mathematical models. Yet, the kinetic description for phy-
cocyanin and EPS formation has been barely addressed and restricted just for low cell densities
(1 g l-1)
2.3.6 State of art – Kinetics models in Arthrospira platensis
In the follow part, it will show the most relevant scientific contributions in the mathematical
modelling of A. platensis. The first approach to mathematical modelling in A. plantesis was
done by Huang and Chen in 1986. They described the A. platensis growth by using a simple
Monod-type model which include just light as limiting factor (Huang and Chen 1986). The
Monod-half saturation constant was 124 µmol m-1 s-1 and µmax of 0.083 h-1. In 1987, a model
which includes photoinhibition was proposed by (Lee and Erickson 1986). A new photoinhibi-
tion constant was incorporated into the Monod mechanism, which has extended the model ca-
pabilities to high illuminations. It was not just until 1994, when Cornet proposed a model that
considered not just light- limitation but also other limiting-factors like nitrate and phosphate
- 26 -
(Cornet et al. 1998). This model was validated until a biomass concentration of 1 g l-1. How-
ever, nowadays higher biomass concentrations are reached. Therefore, these models have to be
extending to high cell densities. A recent research from 2015 developed a model for cell con-
centrations higher that 1 g l-1(Del Rio-Chanona et al. 2015). This model was validated with
experiments from the literature (Xie et al. 2015). The model proposed in this work was also
tested using this experimental points and it will discuss in section 6.7
In almost of the models already mentioned, the biomass composition does not change with the
time, which means that the products of interest, phycocyanin or exopolysaccharides are con-
sider constant during the cultivation. However, as it was already mentioned in section 2.1.2 and
2.13, it knows that biomass compounds variated with the time as the nutrients started to be
consumed. Such variations in biomass activity and composition require a complex description
of the cellular metabolism and a structured approach to the modeling of cell kinetics. However,
in general it is very difficult experimentally to obtain sufficient mechanistic knowledge about
the cell physiology and metabolism for the development of a realistic structured model. More-
over, the mechanism of cell growth is complex and not yet completely understood.
2.4 Modelling photobioreactors features
The site (photobioreactor), where the reactions mentioned above take place, should be described
in detail because some parameters like light, turbulence and mass transfer deepens specifically
of the photobioreactor geometry and operational settings. Furthermore, the current state of art
regarding different methods to simulate light distribution and to estimate the mass transfer co-
efficients in photobioreactors will be presented in the next part. In addition, the influence of
turbulence in microalga culture and the ways to estimate values of turbulence generates in pho-
tobioreactors will be approached.
2.4.1 Modelling light supply in photobioreactors
As we already mentioned, light has to be supplied in every time step to the Equation 6 and it is
known that one of the most important factors that control cell growth in a photobioreactor is
light availability. Perhaps the most unique substrate to model is light since its availability does
not depend just on time, but also on space. The attenuation of light in culture media that contains
cells creates a heterogonous radiation field, which is responsible for the local kinetics (Equation
6). Therefore, it is necessary to consider the effects of the light intensity available in each point
of the reactor on the growth rate.
- 27 -
For low cell densities (<0.1 g l-1) the Beer Lamber law describes the light attenuation by the
cells along the light path. However, for values higher than 0.1 g l-1, the Beer Lamber equation
overestimated the light attenuation by the cyanobacteria because it does not take into account
the scattering coefficient in the algae.
Light attenuation inside of liquid medium depends on two independent phenomena: absorption
by pigments and scattering by the whole cell. The scattering of radiant light energy makes the
mathematical description of light transfer extremely complex, since the available energy in any
point of the reactors derives from the main source of light and from all the directions, because
the light is scattered by the suspension.
One of the most used approaches to simulate light is the two-flux model proposed by Cornet.
This equation is the one-dimensional analytical solution for the radiative transfer model pro-
posed by (Cornet et al. 1998). The most accurate way to simulate the profile in the reactors is
the solution referring to the radiative transfer model in three dimensions, although it consumes
high computer resources.
Once the space light intensities are estimated, the average light intensity to every time step has
to be calculated. There are two methods to estimate this value: the first requires a simple calcu-
lation of the average light value in the light path, whereas the second method requires the con-
crete position of the cyanobacteria in the reactor for each time step. This position can be
matched with the light available in any point of the reactors (Figure 2-9). Although, the last
approach is the more suitable, the lagrangian trajectory information of the cells movement in
the reactor cannot be easily established. The movement of algal cells through light gradients is
very complex, but two recent approaches target this problem theoretically and experimentally.
(Perner et al. 2003) used (CFD) computational fluid dynamic modelling to predict particle tra-
jectories in a tubular photobioreactor equipped with a helical mixer (Zhang et al. 2012) used
(CARPT) computer-automated radioactive particle tracking to actually measure the trajectories
of a small radioactive particle in bubble column and airlift bioreactors (Figure 2-10)
- 28 -
Figure 2-9 Particle track at 0.5 m s−1 (top) superposed with a radial light distribution for two different
biomass concentrations of 0.5 and 2 g l−1 (bottom); the light absorption in the biosuspen-
sion was calculated by means of the hyperbolic model with a light intensity of
IO = 150 μE m−2 s−1 at the reactor surface (Perner-Nochta and Posten 2007).
Figure 2-10 Typical particle trajectories in the draft tube and the split columns - Only one recirculation
is shown for each reactor, while both the front and the top view of the trajectories are
shown respectively in the r–z plane and the cross-sectional plane. Solid lines inside the
figures represent the walls and internals (Luo et al. 2003).
2.4.2 Mass transfer in photobioreactors
The primary source of inorganic carbon for A. platensis is the bicarbonate ion (HCO3-) (Cornet
et al. 1998) enters to cell by an active transport mechanist (Figure 2-11). The intracellular is
the dehydrated via the carbonic anhydrase to CO2, which is incorporate into the Calvin cycle
- 29 -
via the rubisco. This carbon is dispatched for the synthesis of all macromolecules in the cells
from the 3-phosphoglycerate as a key intermediate metabolite.
The bicarbonate present in the standard Zarrouk medium (around 117 mM) is consumed by the
cyanobacteria in order to support its growth. A theoretical value of mass conversion yields of
bicarbonates (2.57 g HCO3- g-1 biomass) was calculated by Cornet et al. it was calculated
based on stoichiometric equations for the biomass formation (Cornet et al. 1998) This yield can
be used to calculate the bicarbonate consumption during the batch cultivation.
With the aim of avoiding carbon limitations and taking advantage of the carbon dioxide cap-
tures, A. platensis cultures may be provided with additional carbon via carbon dioxide injection.
The carbon dioxide should be transferred from the gas phase to the liquid phase. Figure 2-11
shows the steps in the gas mass transfer processes. All these processes from gas phase to liquid
phase can be resumed in one empirical parameter, namely the volumetric mass transfer coeffi-
cient (kla). It is mainly controlled via the flow rate in bubble columns, air-lift and flat plate
photobioreactors (Kantarci et al. 2005). Several studies have demonstrated that the volumetric
mass transfer coefficient increases with gas velocity, gas density and pressure and decreases
with increasing solid concentration and liquid viscosity. Many empirical correlations to calcu-
late the kla are available in the literature and are summarized in the work of (Kantarci et al.
2005).
Figure 2-11 Gas mass transfer (left) and carbon dioxide in water equilibrium and carbon uptake at
different pH and mechanisms (right) (Markou et al. 2013).
Once the dissolved carbon dioxide reacts with the water, it forms other two main species, CO3-
2 and HCO3-. The equilibrium between them could be observed in Figure 2-11. Therefore, de-
pending on the pH, new bicarbonate can be generated from the injected CO2 to support the A.
platensis growth.
- 30 -
2.4.3 Modelling turbulence and light/dark cycles
The culture of cyanobacteria in a photobioreactor should be carried out at a relative high cell
density because this maximizes the biomass productivity and improves the economy in the re-
covering process. However, high cell density requires a level of mixing that ensures a proper
use of the available light, through the light/dark effect, and nutrients (Molina Grima et al. 2000).
In bubble columns and air-lift reactors, similarly to the mass transfer, mixing is controlled via
the flow rate (superficial aeration) and the rheological properties of the fluid.(Rodríguez et al.
2009) (Doshi and Pandit 2005; Pandit and Doshi 2005)
High level of turbulence is characterized by small eddies Figure 2-12. However, smaller eddies
can affect cyanobacteria size growth rate and morphology. The dissipation of the kinetic energy
of turbulence (the energy associated with turbulent eddies in a fluid flow) is the rate at which
the turbulence energy is absorbed by breaking the eddies down into smaller and smaller eddies
until it is ultimately converted into heat by viscous forces. It is expressed as the kinetic energy
per unit mass per second, with units of velocity squared per second (m2 s-3). The damage on the
algae is caused by the shear stress (𝜏), which expresses the parallel force on the surface of the
cell. This force originates from the movement transfer (turbulence) and its value can be calcu-
lated with the following formula that relates energy dissipation rate 𝜀, cyanobacteria diameter
𝑑𝑝 and micro eddy length 𝜆. Therefore, the estimation of energy dissipation rate by experi-
mental technics or simulations is necessary.
There is an evidence that the hydrodynamic shear stress (τ), is the cause of cell damage and
consequently, it mediates the production of reactive oxygen species (ROS) and lipid oxidation
within cells (Rodríguez et al. 2009). For example, the shear sensitivity dinoflagellate Protocer-
atium reticulatum shows agitation-associated shear stress damage threshold lower than 0.16
mPa (Rodríguez et al. 2009). Cyanobacterium are more resistant that dinoflagelletes. In A.
platensis different values that ranged from 0.2 to 1 Pa have been reports as critical shear.
(Mitsuhashi et al. 1995)
Figure 2-12 Schematic of eddies – The higher the energy dissipation rate, the smaller the eddies size
(Sokolichin and Eigenberger 1999).
- 31 -
However, as it was already mentioned, high turbulence is necessary in order to achieve a better
light usage. It is also important to highlight that cyanobacteria, which grow in a photobioreactor
are exposed to natural dark and light cycles as a consequence of the biomass increase in the
photobioreactor. Due to the self-shading effect among algal cells, the light regime inside an
outdoor photobioreactor is characterized by a light gradient with full light at the light-exposed
surface (photic zone) and total darkness in the interior of the photobioreactor (aphotic zone).
The scale-up of photobioreactors cannot be properly done because the light distribution within
the culture is non-homogenous as consequence of this self-shading effects (Camacho et al.
2011). Therefore, as it was already mentioned, light availability is influenced by the position of
the algae in the reactor. By increasing the level of agitation in the reactor, the light availability
per cell seems to increase as result of faster movement between the dark and light zones.
Some studies have found an increase in the biomass productivity in over-saturating illumination
with the increase of the frequency of the light-dark cycles (Luo and Al-Dahhan 2004; Molina
Grima et al. 2000). The magnitude of photo inhibition under continuous strong light is always
greater than under intermittent light. This explains the observation that intermittent light can
provide a higher productivity than the equivalent continuous illumination when the cyanobac-
teria are exposed to light intensities over the saturation point.
Phototrophic microorganism growth can only be sustained if the sufficient amount of reducing
equivalents and energy is produced in the light reaction of the photosynthesis. Under continuous
saturated light intensity, the electrons are produced in a higher rate that the consumption rate in
the dark reaction. The rests of them have to be stored in electron pool and an overflow of elec-
trons will cause photoinhbition, while in a proper intermittent light the electrons generated in
the flash time will be available during the light/dark (L/D) cycle in synchronized way (Rubio
et al. 2003; Wu and Merchuk 2002). However, the size of the electron pool seems only suffi-
cient to achieve full light integration at flash times around 1ms, whereas during longer flash
times the pool will overflow during the light phase, resulting in a loss of photosynthetic effi-
ciency and a decrease in the biomass yield on light (Luo and Al-Dahhan 2004)
As it was already mentioned, depending on the mixing characteristics of the culture suspension,
algal cells will be exposed to different series of light/dark (L/D) cycles. A highly defined mixing
pattern that produces light–dark cycles at a given frequency is required for enhancing produc-
tivity through the flashing-light effect. In contrast, it was concluded that chaotic mixing is not
as effective in enhancing productivity as is organized mixing (Degen et al. 2001; Zhang et al.
2012). Therefore, the uses of photobioreactors with baffles or helical flow promoters have been
- 32 -
proposed in order to create and organized mixing. To sum up, mixing seems to have positive
and negative effects in cyanobacteria culture and they have to be included and linked with the
cyanobacteria kinetics in order to generate a robust model that helps in the cyanobacteria pre-
dictions.
- 33 -
3 Project relevance
Arthrospira (Spirulina) platensis is a filamentous cyanobacterium that has become important
as a source for commercially produced nutraceutical compounds such as phycocyanin, exopol-
ysaccharides (Calcium-Spirulan) and gama-linoleic acid. To understand biological mechanisms
and to optimize production processes, rational design guided by experience is the most common
method currently used. However, experiments are time consuming and expensive and gener-
ally, they generate noisy data. Therefore, predicting the behavior of cyanobacteria during the
culture processes under different culture conditions is highly desirable for both commercial and
scientific reasons and can be an aid in the design of experiments
In batch, the rate of overproduction of metabolites by cyanobacteria is limited or activated by
the depletion of required substrates or by the accumulation of metabolic products and inhibitors.
Therefore, it becomes imperative to identify the parameters that have a significant impact on
product production and to create a mathematical model that can assist the investigation, opti-
mization and scale up of A. platensis growth and phycocyanin and exopolysaccharide produc-
tion in batch cultivation. Although, several mathematical models have been built to simulate
the growth of A. platensis (Cornet et al. 1992; Levert and Xia 2001), most of these studies have
been validated just for low cell densities (<1g l-1) and limitations of carbon or nitrate has been
neglected. In addition, the product formation kinetic and in particular the one for phycocyanin
and exopolysaccharides formation have been barley addressed.
The aim of this study is create a model for higher biomass conditions of A. platensis in bubble
column and then use the model to predict the A. platensis in different cultivation scenarios.
Once the biomass growth is validated, the model will be used to investigate phycocyanin and
exopolysaccharide formation during the batch cultivation under different culture conditions. In
addition, the model will be used to explore a possible controlling nutrient strategy to enhance
the phycocyanin and exopolysaccharide production.
- 34 -
4 Proposed mathematical model
In order to simulate the growth of A. platensis, a macro-scale mathematical model was devel-
oped in two stages (Figure 4-1). The first block incorporates the characterization of the photo-
bioreactor features (i.e. light attenuation, energy dissipation rate and mass transfer coefficient)
by using CFD or/and empirical correlations. This information was then used in the second stage
as input for the kinetic model, which was composed with different equations such as the nitrate
supply, biomass formation and the product formation.
Figure 4-1 Graphical structure of the mathematical model- The model was divided in photobioreac-
tor characterization block and cyanobacteria kinetic model block.
Photobioreactor features Energy dissipation rate
Mass transfer coefficient
Nutrients supply
Biomass formation
Product formation
Light supply
Kinetic model
- 35 -
4.1 Photobioreactor characterization
4.1.1 Energy dissipation rate estimation by using CFD
The energy dissipations rates (𝜀) in the photobioreactor were found by using CFD. In a previous
work, a bubble column with 0.10 m diameter and 0.45 m height and clear liquid height of 0.30
m was simulated using an Eulerian model and the k-𝜀 model for turbulence. The commercial
software Fluent was used to solve the model. All simulation conditions were validated against
the experimental mixing time and gas hold-up (Lobatón et al. 2011). For this work, the same
model and simulation conditions were used for a bubble column with different dimensions:
0.05 m diameter and 0.675 m height. The clear liquid height was 0.45 m and the bubble column
was aerated by air through a sparger (Figure 4-2). The volumetric flow rate was varied in the
range of 1 to 5 vvm. Once the simulations reached the steady state, the energy dissipation rate
ε was obtained as the average of all grid points.
Figure 4-2 Bubble column mesh to perform the CFD simulations - 0.05 m diameter and 0.675 m
height.
Kolmogorov’s theory describes how energy is transferred from larger to smaller eddy, how
much energy is contained by eddies of a given size and how much energy is dissipated by eddies
of each size. Furthermore, the smaller the eddy, the more damage on the cell occurs. The dam-
age on the algae is caused by the shear stress, which expresses the parallel force on the surface
- 36 -
of the cell. This force originates from the movement transfer (turbulence) and its value can be
calculated with the following formula that relates energy dissipation rate 𝜀, cyanobacteria di-
ameter 𝑑𝑝 and micro eddy length 𝜆.
Equation 11: 𝜆 = (𝜇𝑙
𝜌𝑙)
3
4. 𝜀−
1
4
Equation 12: 𝜏 = 0.0676. (𝑑𝑝
𝜆) . (𝜌𝑙. 𝜇𝑙. 𝜀)0.5
4.1.2 Light absorption
Light was modeled with the radiative transfer model (one-dimensional two-flux model)
(Cornet et al. 1998) for a bubble column with a radius of 0.025 m:
Equation 13: I(r, t) = Is ×1r
R
×2∗cos h(δ×
r
R)
cos h(δ)+α×sin h(δ)
The coefficients α and δ show the dependence of light attenuation from the biomass
concentrations and from the phycocyanin mass fractions:
Equation 14: α = [Ea∗(Zpc+0.009)
(Ea∗(Zpc+0.009)×+Es)]
1/2
Equation 15: δ = [𝐸𝑎 ∗ (Zpc + 0.009) + 𝐸𝑠] × xt × α × R
4.1.3 Mass transfer coefficient estimation
The mass transfer coefficient was calculated by using an empirical correlation for bubble col-
umns proposed by (Kantarci et al. 2005).
Equation 16: 𝑘𝑙𝑎 = 0.467 × 𝑣𝑔0.88
Equation 17: 𝑣𝑔 =𝑄
𝐴𝑐𝑠
4.2 Macroscale mathematical model
A mathematical model for A. platensis growth and phycocyanin formation was developed under
the following assumptions:
1. A well-mixed homogeneous model for bubble columns operated in batch mode for the
liquid phase and continually for the gas phase. The depletion of carbon dioxide in the
gas phase was neglected due to short gas residence time in the short-sized bubble col-
umn.
- 37 -
2. The relationship between the CO2 partial pressure and its equilibrium in the liquid phase
was simplified with Henry´s law. Consequently, the changes within the dissolved car-
bon dioxide concentration were modeled using the following equation:
Equation 18: 𝑑𝑐
𝑑𝑡= 𝑘𝑙𝑎 × (
𝑃×𝐶𝐶𝑂2
𝐻𝐶𝑂2
− 𝑐)
3. The changes in the bicarbonate depend on the rate of microalga consumption:
Equation 19: 𝑑𝑏
𝑑𝑡=
𝑑𝑐
𝑑𝑡− 𝑦𝑏
𝑥
×𝑑𝑥
𝑑𝑡
4. In cyanobacteria cultures, the changes in pH occur mainly as a result of carbon con-
sumption. However, the pH variation derived from other nutrients or degradation of the
excreted metabolites can be neglected (Camacho Rubio et al. 1999). The pH calcula-
tions were based on the Henderson-Hasselbalch equation:
Equation 20: 𝑝𝐻 = 𝑝𝑘 + 𝑙𝑜𝑔 ([𝑏]
[𝑐])
5. The biomass was modeled using a kinetic Monod model with light, bicarbonate and
nitrate as limitations:
Equation 21: 𝑑𝑥𝑎
𝑑𝑡= µmax (𝑝ℎ) ×
𝐼
𝐼+𝐾𝑖+𝐼2
𝐾𝑖𝑝
×𝑏
𝑏+𝐾𝑏×
𝑛
𝑛+𝐾𝑛× 𝑥𝑎 − 𝑀𝑒 × 𝑥𝑎
6. 𝑀𝑒 is a maintenance constant, which accounts for cellular damage due to adverse envi-
ronments, i.e. high shear stress. Wu and Merchuk found that the shear stress below crit-
ical level does not have any effect, whereas beyond the critical shear stress, the mainte-
nance term increases exponentially (Wu and Merchuk 2002). The CFD results in this
work shows by using 1 vvm, the maximum shear stress calculated was 0.3 Pa, which is
below the critical shear stress (1 Pa) reported in A. platensis. Therefore, the 𝑀𝑒 term
was neglected.
Equation 22: 𝑀𝑒 = 𝑀𝐸̅̅̅̅̅ × 𝑒𝑘𝑚(𝜏−𝜏𝑐)
7. Under nitrate limitation conditions, the continuous increase in the biomass concentra-
tion results from the accumulation of intracellular glycogen and exopolysaccharides.
Therefore, Equation 21 was modified to include this effect and the new equation was
described as follow:
Equation 23: 𝑑𝑥
𝑑𝑡= µmax (𝑝ℎ) × (
𝐼
𝐼+𝐾𝑖+𝐼2
𝐾𝑖𝑝
×𝑏
𝑏+𝐾𝑏×
𝑛
𝑛+𝐾𝑛+
𝑍𝑝𝑐
𝑍𝑝𝑐+𝐾𝑝𝑐×
𝐾𝑛
𝑛+𝐾𝑛) × 𝑥
8. According to Cornet et al, the mass fraction of phycocyanin (Zpc) remains constant in
the exponential or linear phase before the appearance of nutrient limitations (Cornet et
al. 1998). However, the experimental results in this work show that the mass fraction of
- 38 -
phycocyanin varies also in the exponential phase. Therefore, an equation that describes
the variation of the phycocyanin content in the cell was set up:
Equation 24: 𝑑𝑧𝑝𝑐
𝑑𝑡= 𝑅𝑝𝑐 × (
𝐾𝑙𝑖
𝐼+𝐾𝑙𝑖 − (
𝐼
𝐼+𝐾𝑙𝑖+
𝐾𝑛
𝑛+𝐾𝑛+
𝐾𝑏
𝑏+𝐾𝑏) ) × 𝑧𝑝𝑐
9. The nitrate and phosphate consumption was described using the following equation:
Equation 25: 𝑑𝑛
𝑑𝑡= −𝑌𝑛
𝑥×
𝑑𝑥
𝑑𝑡 Equation 26:
𝑑𝑝
𝑑𝑡= −𝑌𝑝
𝑥×
𝑑𝑥
𝑑𝑡
The model was simulated in Matlab and the parameters and conditions used for simulation are
shown in Table 4-1. The program code is included in the annex 1.
- 39 -
Table 4-1 Summary of parameters and conditions used in the simulation of Arthrospira platensis
Parame-
ter
Value
Range
Reference/
Comments
Parame-
ter
Value
range
Reference/
Comments
Consumption yields Io 60-600 experimental
condition
yb/x 2.57 (Cornet et al.
1998) No 0.91.82
experimental
condition
yn/x 0.45-
0.56
(Cornet et al.
1998) Xo 0.3-0.6
experimental
condition
yp/x 0.024 (Cornet et al.
1998) 𝑪𝑪𝑶𝟐
0.035-3 experimental
condition
Empirical parameters Bo 9.8 experimental
condition
Ki 72-120
(Chen et al. 2013;
Cornet et al.
1998) P 1.0
experimental
condition
Kip 400 (Del Rio-Chanona
et al. 2015) po 0.2
experimental
condition
Kil 28 estimated from
experimental data R 0.025
experimental
condition
Kb 3×10-6 (He et al. 2012) Bicarbonate/carbonate system con-
stants
Kn 1×10-2
5.3×10-3
(Cornet et al.
1998; Levert and
Xia 2001) pK 6.4
(Keymer et al.
2014)
kla 30
estimated from
empirical correla-
tion Cp 4.5
(Cornet et al.
1998)
µmax 0.073-
0.09
(Chen et al. 2013;
Cornet et al.
1998)
𝐇𝐂𝐎𝟐 30.04 (He et al. 2012)
Ea 4300
(Cornet et al.
1998)- estimated
from experi-
mental data
kca 8.9×10-
3 (Kern 1960)
Es 730
(Cornet et al.
1998)- estimated
from experi-
mental data
Empirical parameters for turbulence
Kpc 2×10-4 estimated from
experimental data 𝝉𝒄 0.3
(Wu and
Merchuk 2002)
Rpc 0.02-
0.038
estimated from
experimental data km
1.6×10-
3
(Wu and
Merchuk 2002)
Initial conditions 𝑴𝑬̅̅ ̅̅ ̅ 0.0-
0.059
(Wu and
Merchuk 2002)
- 40 -
5 Materials and methods
5.1 Microalga and media composition
Arthrospira platensis N-39 was obtained from NIES, Japan and pre-cultured in Zarrouk Me-
dium. The medium is composed of (per litre): 13.61g NaHCO3, 4.03g Na2CO3, 2.5g NaNO3,
1g K2SO4, 1g NaCl, 0.5g K2HPO4, 0.2g MgSO4.7H2O, 0.04g CaCl2.2H2O and 5ml of trace
metal solution, which consists in (per litre): 0.7g FeSO4.7H2O, 0.8g EDTA, 0.01g H3BO3,
0.002g MnSO4.4H2O, 0.001g ZnSO4.7H2O, 0.001g Co(NO3)2.6H2O, 0.001g Na2MoO4.2H2O.
5.2 Preculture
The preculture was grown in Erlenmeyer and constantly agitated by mixer plate at 110 rpm,
25°C and 40 µmol m-2 s-1. Cells in exponential growth were used for the following experiments.
5.3 Photobioreactor setup
A. platensis was cultivated in 1 L bubble column photobioreactor (Figure 5-1) (Walter et al.
2003) with a gas flow rate of 48 l h-1(1vvm) and 240 l h-1 (5vvm). The working volume was 0.8
L. The gas supplied was just air (0.035% (v/v) CO2) or mixtures of air and CO2, depending on
the experimental trial. All the trials were carried out at 30°C, form 60 to 700 µmol m-2 s-1 of
light intensity (illuminated by fluorescent lamps surrounding the reactor), initial biomass from
0.3 to 0.5g l-1 and gauge pressure of 1 bar. The inlet and outlet flows of the reactors were con-
nected with a micro filter (Midisart 2000 0.2µm PTFE, Sartorius Stedim) during the whole
cultivation time in order to keep the process in sterile conditions.
In preliminary trials, it was observed, that the liquid phase in PSM decreased in high flow rates.
Therefore, in order to reduce the liquid losses in the experiment with high flow rates, a humid-
ifier in the in inlet and a cooling system in the outlet were used.
- 41 -
Figure 5-1 Photobioreactor screening module (PSM) (Walter et al. 2003).
The function of the humidifier was to saturate the inlet air of water in order to decrease the
aqueous mass transfer inside the reactors, avoiding the reactor`s level variation. A heat plate
was used in addition to the display in order to optimize its efficiency. The mass of water in
saturated air increases by heating, therefore, its usage can ensure the maintenance of the reac-
tor's level. On the other hand, the overheating could increase the aqueous mass transfer from
the gas to liquid phase, enhancing the culture level.
A cooling system was set up after the outlet in order to condense the water in the gas phase,
avoiding the exit of water (Figure 5-2). The both inlet and outlet flows of the PSM were con-
nected with a micro filter (Midisart 2000 0,2µm PTFE, Sartorius Stedim) during the whole
cultivation time in order to keep the process in sterile conditions.
- 42 -
Figure 5-2 Cultivation set up with a gas humidifier in the inlet and cooling system in the outlet.
5.4 Analytic determinations
5.4.1 Biomass quantifications and pH measurements
Culture samples were daily collected from the bubble columns in sterile conditions. The bio-
mass (g l-1) was measured directly after a biomass lyophilisation process. In addition, the optical
density was determined by measuring the absorbance at a wavelength of 750 nm using a spec-
trophotometer (Specord 210-A, Shimadzu). The pH was also measured for every sample with
the pH-Electrode MP 220 (Mettler Toledo).
5.4.2 Nitrate determinations
The nitrate concentration in the medium was determined by a colorimetric method. The cali-
bration between the absorbance and nitrogen concentration was established using sodium ni-
trate as the standard and they were determinate by the absorbance at 210 nm.
5.4.3 Phycocyanin determinations
Phycocyanin measurements were done as following: samples were centrifuged at 4000 rpm, 25
°C and 10 minutes and the medium was discarded and the biomass was freeze-dried. Further-
more, the dried biomass was weighed and used to extract the phycocyanin content. 0.01g or
- 43 -
0.6g dried weight of the total dried biomass was disrupted by Tissuelyser at 50Hz for 3 minutes
and then suspended into 4 ml of 0.15 M phosphate buffer and 0.4ml of streptomycin. This
suspension was maintained at 4 °C for one hour and agitated every 30 minutes. After this pro-
cedure, it was centrifuged at 4000 rpm, 10 °C and 10 minutes and the blue supernatant was
collected. The absorbance was measured at wavelength of 615 nm or 620 nm and 652 nm using
a spectrophotometer (Specord 210-A, Shimadzu) and the phycocyanin concentration was cal-
culated according to the following formula (Patel et al. 2005):
Equation 27: Pc =OD615−0.474 ×OD652
5.34
5.4.4 Exopolysaccharides (EPS) quantifications
Exopolysaccharide measurements were done as following: samples were centrifuged at (4000
rpm, 25) and the supernatant was used to determinate EPS photometric with the anthrone assay
proposed by (Laurentin and Edwards 2003) using galactose solution as a standard reference.
Figure 5-3 shows a 96 well plate with the galactose solution (columns 1 to 3) and various su-
pernatant treated with anthrone in different trails (columns 4 to 12).
Figure 5-3 96-well plate with reference and culture supernatant in the different experiments.
- 44 -
5.5 Experimental plan
In order to test the model predictions, an experimental plan that changes one of the culture
conditions (carbon dioxide, flow rate and light) and leaves the others parameters fixed has been
developed Table 5-1. It is important to highlight that these experiments were planned in order
to test the model fitting performance. All the experiments were done by duplicate.
Table 5-1 Experimental plan
Parameter
Experiment
Carbon
dioxide
(%)
Flow
rate
(vvm)
Light
(µmol m-2 s-1)
Nitrate
(g l-1)
Bicarbonate/
Carbonate
(g l-1)
1. Flow rate 0.035 1 and 5 60 1.8 9.88/1.7
2. Carbon
dioxide 0.8 and 3 1 60 1.8
9.88/1.7
9.88/1.7
9.88/1.7
3. Light 3 1 60 and 120 1.8 9.88/1.7
4. Total nitrate
depletion 1.4 1 60 and 400 1.8 9.88/1.7
5. Nitrate vali-
dation 1.4 1 600 0.9 9.88/1.7
6. Nitrate Fed-
batch additions 1.4 1 600
0.9 + addi-
tions
9.88/1.7
- 45 -
6 Results
6.1 Photobioreactor computational fluid dynamics characterization:
Energy dissipation rates and liquid velocities
The simulation of computational fluid dynamics (CFD) in the photobioreactor (Figure 6-1)
shows that the average energy dissipation rate 𝜀 has slightly increased from 0.025 to 0.03 m2 s-
3. This is the result of the increase in the gas flow rate from 1 to 2 vvm. Subsequently, 𝜀 shows
a drastic increase to 0.15 m2 s-3 for a flow rate of 5 vvm.
Figure 6-1 Average energy dissipation rates and average fluid velocities for different gas flow rates
in the photobioreactor. Each data point is an average from all of the local values in the
mesh.
One of the advantages of using CFD is the possibility to visualize the local hydrodynamic val-
ues, which supply detailed information at every point of the photobioreactor instead of an av-
erage global value. Figure 6-2 shows the local 𝜀 in a front view of the reactor for volumetric
flow rates of 1 vvm and 5 vvm. As we see, at 1 vvm all the local values are lower than 0.1 m2
s-3. However, at 5 vvm there are two zones: one with local values less than 0.1 m2 s-3 and another
with 𝜀 values that range from 0.1 to 0.5 m2 s-3. In other words, by using 5 vvm, the higher 𝜀
seems to be associated with the bubble plume. These results reflect the literature, which states
that in bubble columns 𝜀 commonly varies within the range of 0.1 to 0.4 m2 s-3(Rodríguez et al.
1 2 3 4 50
0.05
0.1
0.15
vvm
1 2 3 4 50.05
0.1
0.15
0.2
Energy dissipation rate m2 s
-3
Liquid velocity m s-1
- 46 -
2009) and in stirred tanks the local 𝜀 is higher in the vicinity of impellers (Rodríguez et al.
2009) than in the bulk of the reactor.
Figure 6-2 Local energy dissipation rates in a front view of the in the photobioreactor for different
gas flow rates (1 vvm and 5 vvm) after 40 s of simulation time.
The damage to the algae is caused by the shear stress which expresses a parallel force on the
surface of the cell. This force originates from the movement transfer (turbulence) and its value
can be calculated using the formula presented above in section 4.1 that for the energy dissipa-
tion rate 𝜀, micro eddy length (𝜆) and cyanobacteria size (𝑑𝑝). The cyanobacterium size was
assumed to be 200 µm. Using 1 vvm, the maximum shear stress calculated with these equations
was 0.3 Pa, which is below the critical shear stress reported in A. platensis (see section 2.4.1).
As seen in Figure 6-2, in the green, yellow and red zones, 5 vvm generates higher energy dissi-
pation rates, which imply higher shear stresses. The values for the shear stress range from 0.3
to 1.34 Pa in the bubble plume area. This result is analyzed later in this work in the cultivation
section.
- 47 -
Along with better mass gas transfer, one of the advantages of increasing the flow rate is that the
cyanobacteria respond better to the light and dark cycles in the reactor. Assuming that cyano-
bacteria are particles that move with the fluid, the liquid velocities and algae trajectories deter-
mine the time of the transition of cyanobacteria between the illuminated and dark zones. Fur-
thermore, the availability of light to the entire cell wall is guaranteed by higher liquid velocities,
which trigger a faster algal rotation. Figure 6-3 shows that from the lowest flow rate, 1 vvm, to
the highest, 5 vvm, the average liquid velocities range from 0.05 to 0.2 m s-1, and displays the
local fluid velocities in a front view for the volumetric flow rates of 1 vvm and 5 vvm. This
hydrodynamic information (energy dissipation rates and liquid velocities) from the photobiore-
actor-screening module (Figure 5-1) is discussed later along with the cyanobacteria cultivation
results in the section “influence of flow rate on biomass”.
Figure 6-3 Local liquid velocities in 1 vvm and 5 vvm in a front view of the in the photobioreactor
for different gas flow rates (1 vvm and 5 vvm) after 40 s of simulation time.
- 48 -
6.2 Biomass cultivation results
Mathematical models are useful tools to predict the behavior of complex systems such as cya-
nobacteria batch cultivation. In this type of cultivation, the nutrients are depleted during the
process, leading to different cyanobacteria compositions. Nonetheless, before a mathematical
model can be applied in practice, it should first be verified against experimental data. In this
work, the proposed mathematical model was tested with the experimental biomass concentra-
tions for the culture conditions indicated in Table 5-1
After the model was validated, it was used to investigate phycocyanin and exopolysaccharide
formation during batch cultivation. It was also used to formulate a possible strategy to enhance
phycocyanin production.
6.2.1 Gas flow rate experiments and model validation
The flow rate validation was carried out with a fixed carbon dioxide concentration of 0.035%
and an illumination of 60 µmol m2 s-1. Two gas flow rates (1 vvm and 5 vvm) were experimen-
tally tested and the experimental biomass concentrations were used to test the model fitting
performance. The same experimental conditions presented in Table 5-1 were used as initial
conditions in the simulations. The increase in flow rate from 1vvm to 5 vvm resulted in an
increase in the growth rate and final biomass of A. platensis (Figure 6-4).
The model simulations (solid and dotted lines) are able to capture this trend. In addition, Figure
6-5 shows the predicted internal light in the reactor. As we see, after 100 hours of cultivation
there is a dark zone that represents almost 60% of the total reactor volume and an illuminated
area that represents the remaining 40% of the reactor volume. Figure 6-5 shows that at 5 vvm
the light is slightly more attenuated as a result of higher growth compared to the 1 vvm reactors.
The mass transfer coefficient (kla) expresses the rate at which CO2 is converted from the gas
phase to the liquid phase. An increase in the mass transfer coefficient along with the increase
of the flow rate is observed in bubble columns (Kantarci et al. 2005). Furthermore, Figure 6-6
shows that the pH increased during the cultivation and moved out of the optimal range (8.5-
9.5). However, this increase was less pronounced with the volumetric flow at 5 vvm.
- 49 -
Figure 6-4 Simulated and experimental growth of A. platensis in different gas flow rates. The lines
show the results from the simulation of the following conditions: 60 µmol m-2 s-1, 0.035 %
carbon dioxide, 30°C, which corresponds to the same experimental conditions implement
in the PSM cultivation.
Figure 6-5 Light attenuation after 100 hours of cultivation in different gas flow rates. The lines show
the results from the simulation of the following conditions: 60 µmol m-2 s-1, 0.035 %
carbon dioxide, 30°C, which corresponds to the same experimental conditions imple-
ment in the PSM cultivation.
- 50 -
Figure 6-6 Simulated and experimental pH in different gas flow rates. . The lines show the results
from the simulation of the following conditions: 60 µmol m-2 s-1, 0.035 % carbon di-
oxide, 30°C, which corresponds to the same experimental conditions implement in the
PSM cultivation.
6.2.2 Carbon dioxide experiments and model validation
The carbon dioxide validation was carried out with a fixed volumetric flow rate of 1 vvm and
60 µmol m-2 s-1. In the first trial, a CO2 concentration of 3 % and 0.035 % was simulated and
tested against experimental biomass concentrations (Figure 6-7). There was found to be a good
correlation between the model and the experimental data. Figure 6-7shows a faster growth and
two-fold increase in the final biomass in the cultivation with 3% CO2 compared to 0.035 %
CO2. This can be explained by the high pH in the cultivation with 0.035 % CO2 (Figure 6-7)
compared to that in the 3 % concentration.
- 51 -
Figure 6-7 Simulated and experimental biomass in 3 % and 0.035 % carbon dioxide (Top) Simulated
and experimental pH at 3 % and 0.035 % carbon dioxide (Bottom). The lines show the
results from the simulation of the following conditions: 60 µmol m-2 s-1, 1 vvm, 30°C,
which corresponds to the same experimental conditions implement in the PSM cultiva-
tion.
After further simulations, an optimal carbon dioxide concentration of 0.8 % was chosen for the
next experiment, since the model forecast that this concentration would lead to an optimal pH
of approximately 9.3.
Figure 6-8 shows the growth curve using 3 % and 0.8 % CO2. The same biomass growth was
found in both cases. In addition, Figure 6-8 shows a pH of approximately 9.5 at 0.8 % and 8.5
at 3 %. Figure 6-9 shows the predicted dissolved carbon dioxide using 3 % and 0.8 %. In both
cases, there is an increase until it reaches a steady state.
- 52 -
Figure 6-8 Simulated and experimental biomass in 3 % and 0.8 % of carbon dioxide (Top) Simulated
and experimental pH at 3 % and 0.8 % carbon dioxide (Bottom). The lines show the
results from the simulation of the following conditions: 60 µmol m-2 s-1, 1 vvm, 30°C,
which corresponds to the same experimental conditions implement in the PSM cultivation
Figure 6-9 Simulated dissolved carbon dioxide in 3 % and 0.8 % of carbon dioxide. The lines show
the results from the simulation of the following conditions: 60 µmol m-2 s-1, 1 vvm,
30°C, which corresponds to the same experimental conditions implement in the PSM
cultivation.
- 53 -
6.2.3 Light intensity experiments and model validation
In order to test the model’s capability and to predict the A. platensis growth when the light
increases, the following experiments were conducted. A simulation and experimental trial with
light intensities of 60 and 120 µmol m-2 s-1 were carried out and an optimal carbon dioxide
concentration of 1.4% was calculated in order to maintain theoretically enough carbon and a
pH of 9.0. Figure 6-10 shows the predictive capability of the model based on the results from
the increase in light intensity. At light intensities of 120 µmol m-2 s-1, the biomass productivity
was two times greater than the experimental results at 60 µmol m-2 s-1.
Figure 6-10 Simulated and experimental growth at different incident light intensity on PSM surface.
The lines show the results from the simulation of the following conditions: 1.4 % carbon
dioxide, 1 vvm, 30°C, which corresponds to the same experimental conditions implement
in the PSM cultivation.
Figure 6-11 shows the simulated results from light attenuation using different incidents light
intensity on PBR surface. At the end of the cultivation, it can be observed that the reactor with
120 µmol m-2 s-1 has slightly increased in light, perhaps as a consequence of the nitrate deple-
tion, which may generate changes in the cyanobacteria harvesting proteins. These phenomena
- 54 -
will be addressed in more detail in the section regarding phycocyanin biosynthesis. This un-
physical rise in the light supply generates the unreal increment in the simulated biomass by
using 120 µmol m-2 s-1 (Figure 6-10). In sum, the use of high light intensities leads to higher
growth rates coupled with faster nutrient consumption.
Figure 6-11 Internal light intensity at different incident light intensity on PSM surface. The lines show
the results from the simulation of the following conditions: 1.4 % carbon dioxide, 1 vvm,
30°C, which corresponds to the same experimental conditions implemented in the PSM
cultivation.
Figure 6-12 shows the predicted nitrate consumption in the cultivation. The main nitrogen
source for A. platensis is the nitrate (NO3-) ion, which is 1.8 g l-1 (29 mM) in the standard
spirulina medium. According to the model, nitrate depletion occurs after 250 hours in the cul-
tivation with 120 µmol m-2 s-1, whereas in the cultivation with 60 µmol m-2 s-1 some nitrate still
remains after 300 hours of cultivation. Different nutrient concentrations over the course of cul-
tivation can lead to different cyanobacteria compositions. This is discussed below in the section
about phycocyanin formation and degradation.
- 55 -
Figure 6-12 Simulated nitrate at different incident light intensity on PSM surface. The lines show the
results from the simulation of the following conditions: 1.4 % carbon dioxide, 1 vvm,
30°C, which corresponds to the same experimental conditions implement in the PSM
cultivation.
6.3 Product formation results
Figure 6-13 shows a comparable phycocyanin mass fraction using various concentrations of
3 %, 0.8 %, 0.035 % CO2 in the experiments conducted at 60 µmol m-2 s-1. The figure shows
that when using low light intensities (60 µmol m2 s-1) phycocyanin increases in the cell until
150 hours, at which point it reaches a steady state. Furthermore, all carbon dioxide concentra-
tions present the same trend in the growth curve.
It is important to highlight that at the beginning of the cultivation some phycocyanin degrada-
tion must be accounted for by the photoadaptation process described above. Thus, collecting
data at the beginning of the experiment impeded the analysis in the first 50 hours. However,
this issue was overcome in a further experiment that is presented and discussed in sections 6.5
and 7.7.
- 56 -
Figure 6-13 Experimental phycocyanin mass fractions at different carbon dioxide concentrations. Ex-
perimental conditions implemented in the PSM cultivation: 1 vvm, 30°C.
A. platensis was cultivated to examine the effect of this factor on growth and product generation
at a higher light intensity. A trial experiment with a light intensity of 400 µmol m-2 s-1 was set
up. Figure 6-14 shows a comparable phycocyanin mass fraction using 60 µmol m-2 s-1 and 400
µmol m-2 s-1, with a higher phycocyanin mass fraction in the first case. At 60 µmol m-2 s-1, the
figure shows that phycocyanin content increased in the cell and after 180 hours its production
stopped and remained stable until the conclusion of the cultivation. Meanwhile, with a light
intensity of 400 µmol m-2 s-1, phycocyanin also built up in the cell, but after 96 hours its pro-
duction stopped it began to degrade.
- 57 -
Figure 6-14 Experimental phycocyanin mass fractions at different incident light intensity on PSM
surface. Experimental conditions implemented in the PSM cultivation: 1.4 % carbon di-
oxide, 1 vvm, 30°C.
Figure 6-15 shows that at light intensities of 400 µmol m-2 s-1, the biomass productivity was four
times greater than the experimental results at 60 µmol m-2 s-1. It is important to highlight that
(Xie et al. 2015) reported photoinhibition in the cultivation of A. platensis at 450 µmol m-2 s-1.
This was supported by an observation of a change in color from green to white during the first
three days of the cultivation. However, in this work, there was no evidence of photoinhibition.
The discrepancy in these results can be explained by the different initial cell densities used in
both cases. Figure 6-15 also shows the predicted nitrate consumption in the cultivation using
the model. According to the model, nitrate depletion occurs after 100 hours in the cultivation at
400 µmol m-2 s-1, whereas in the cultivation at 60 µmol m-2 s-1 some nitrate still remains after
250 hours of cultivation. In order to verify the hypothesis concerning nitrate limitation, a new
experiment was set up and is described in the next section.
- 58 -
Figure 6-15 Experimental biomass at different incident light intensity on PSM surface. (Top) Simu-
lated nitrate at different incident light intensity on PSM surface. (Bottom). The lines show
the results from the simulation of the following conditions: 1.4 % carbon dioxide, 1 vvm,
30°C, which corresponds to the same experimental conditions implement in the PSM cul-
tivation
6.4 Nitrate model validation
In order to test the model’s prediction capability regarding nitrate consumption, an experiment
with 600 µmol m-2 s-1 of light intensity and an initial nitrate concentration of 0.9 g l-1 was set
up. Figure 6-16 shows the experimental and predicted biomass results for cultivation with at
600 µmol m-2 s-1. The model shows good agreement with the experimental data at the beginning
of the cultivation. Furthermore, the model demonstrates good agreement when predicting the
nitrate concentration in the medium. Figure 6-16 shows that nitrate depletion occurs after 50
hours in the cultivation. The theoretical yield of 0.48 g NO3- per g biomass is accurate to calcu-
late the nitrate consumption.
- 59 -
Figure 6-16 Experimental and simulated biomass in 600 µmol m-2 s-1 (Top) Experimental and Sim-
ulated nitrate in 600 µmol m-2 s-1 (Bottom). The lines show the results from the simulation
of the following conditions: 1.4 % carbon dioxide, 1 vvm, 30°C, 0.9 g l-1 initial NO3-,
which corresponds to the same experimental conditions implement in the PSM cultiva-
tion.
6.5 Effects of nitrate on phycocyanin and exopolysaccharides production
A new experiment was set up with a light intensity of 600 µmol m2 s-1 and two nitrate condi-
tions. The first was named ‘the control’ and had an initial nitrate concentration of 0.9 g l-1. The
second had the same initial nitrate concentration but different nitrate feeds at 29, 52, 76, 99
hours. Nitrate, phycocyanin and exopolysaccharides were measured during the cultivation.
Figure 6-17 shows the biomass in the control and in the fed batch cultivation. Between 50 to
150 hours, a higher biomass was found in the control, although the measurements show that the
nitrate was completely depleted. Moreover, in the control experiment the nitrate depletion oc-
curs after 50 hours in the cultivation (Figure 6-17).
- 60 -
Figure 6-17 Experimental biomass in control and nitrate Fed batch experiment (Top) Experimental
and simulated nitrate in control and nitrate Fed batch experiment (Bottom) The lines show
the results from the simulation of the following conditions: 600 µmol m-2 s-1, 1.4 % carbon
dioxide, 1 vvm, 30°C, 0.9 g l-1 initial NO3-, which corresponds to the same experimental
conditions implement in the PSM cultivation.
In addition, the slightly lower biomass concentration in the fed batch was probably also as a
result of the higher phycocyanin concentration (Figure 6-18). According to (Cornet et al. 1992)
the higher the phycocyanin mass fraction, the higher the light absorption, which consequently
leads the light being highly attenuated. In the nitrate fed batch experiment, the phycocyanin
mass fraction was higher than in the control experiment between 50 to 20 hours of cultivation
(Figure 6-18). Therefore, the higher light attenuation can be the explanation to the lower bio-
mass in the fed batch experiment between these period of time.
- 61 -
Figure 6-18 Phycocyanin mass fractions in control and nitrate fed-batch experiment. Experimental
conditions implemented in the PSM cultivation: 600 µmol m-2 s-1,1.4 % carbon dioxide,
1 vvm, 30°C, 0.9 g l-1 initial NO3-.
With the nitrate additions, the phycocyanin mass fraction was expected to remain at least con-
stant during the whole cultivation. However, the phycocyanin decreased after the third addition
(76 hours), but at a slower rate than in the control experiment (Figure 6-18). Limitations of other
macronutrients such as carbon may be the reason for the phycocyanin decrease. This is dis-
cussed further in section 7.5. Nonetheless, phycocyanin mass fractions and productivities were
enhanced by the nitrate additions as compared to the control cultivation.
Concerning the exopolysaccharide (EPS) formation, the nitrate addition experiment (Figure
6-19) shows a greater EPS mass fraction than in the control experiment. In the control experi-
ment the EPS mass fraction (around 20 mg g-1 of biomass) remains stable throughout the culti-
vation, whereas in the nitrate addition experiment there was a slight increase from 25 mg g-1
to 50 mg g-1 until 220 hours of cultivation. After this time, there was an incremental increase
in the EPS from 50 mg g-1 to 100 mg g-1. Multiplying the mass fraction by the biomass in the
reactor shows the same trends as in the mass fraction results. A maximum space-time yield of
(32 mg l-1 d-1)) was reached in the experiment with nitrate additions.
- 62 -
Figure 6-19 Exopolysaccharides mass fractions in control and nitrate fed-batch experiment. Experi-
mental conditions implemented in the PSM cultivation: 600 µmol m-2 s-1,1.4 % carbon
dioxide, 1 vvm, 30°C, 0.9 g l-1 initial NO3-
6.6 Phycocyanin kinetic model
Figure 6-20 shows the simulations and the experimental results for the phycocyanin mass frac-
tion in different light intensity and nitrate conditions. In all trials, simulations show a decrease
in phycocyanin up to 50 hours as result of high illumination at the beginning of the cultivation.
After 50 hours, there is an increase in the mass fraction that concludes when the nitrate and/or
carbon limitation appears. The kinetic mechanism proposed in this work for phycocyanin for-
mation simulated the experimental results in a suitable manner. A detailed discussion of the
kinetic model is presented in section 7.7.
- 63 -
Figure 6-20 Experimental and simulated phycocyanin mass fractions in different experimental condi-
tions. The lines show the results from the simulation of the following conditions:,1.4 %
carbon dioxide, 1 vvm, 30°C, which corresponds to the same experimental conditions
implement in the PSM cultivation.
6.7 Literature data simulations
The model was used to simulate two experiments from the literature. The first, a pond cultiva-
tion (d = 5 m), was performed in a greenhouse facility at the Fisheries Science and Technology
Center, Pukyong National University, Goseong, South Korea (FSTC) from May 21st, 2014 to
June 24th, 2014. The microalgae were grown in SOT media at total volume of 15,000 L, inoc-
ulated with 1000 L of subculture from hanging bag cultivation, at an initial pH of 8.68 under
- 64 -
sunlight with an average of approximately 110 µmol m−2 s−1 (a sunny day), at 20 – 35 °C with
an initial OD at 560 nm of 0.05 and a stirring speed of 10 - 15 min−1.(Reichert 2016). Figure
6-21 shows the experimental results compared to the simulation data. Although the model is
able to capture the growth curve trend, some experimental points between 200 hours and 500
hours are out of the range of prediction. It is important to highlight that the model works with
constant values of light and temperature, which can explain the deviation with the experimental
results in outdoor cultivations. Furthermore, the model does not include water evaporation,
which may also have influenced the experiment results.
Figure 6-21 Simulated and experimental biomass from A. platensis (data from Reichert 2016). The
experimental points correspond to cultivation in an open pond with a diameter of 5 m.
The lines show the results from the simulation of the same experimental conditions ap-
plied by Reichert (2016).
The second experiment was a cultivation under control conditions performed by (Xie et al.
2015). The photobioreactor (PBR) used to cultivate the A. platensis was a 1-L glass vessel (15.5
cm in length and 9.5 cm in diameter) equipped with an external light source (14 W TL5 tungsten
filament lamps, Philips Co., Taipei, Taiwan) mounted on both sides of the PBR. The microalga
was pre-cultured and inoculated into the PBR with an inoculum size of 0.08-0.24 g l-1. The
- 65 -
PBRs were operated at 28 °C, pH 9.0, and an agitation rate of 400 rpm under a light intensity
of approximately 75-450 µmol m2 s-1. Serving as the sole carbon source, 2.5 % CO2 at 0.2 vvm
was fed into the microalgal culture continuously during cultivation (Xie et al. 2015). The bio-
mass simulation results (Figure 6-22) show good agreement until 350 hours of cultivation. After
that point, the model predicts an unphysical steep rise as result of the phycocyanin degradation.
The model was also able to predict the nitrate consumption (Figure 6-22) with a good correlation
between the experimental data and the model simulations. In addition, the model was used to
describe phycocyanin formation. Figure 6-23 shows an increase in the phycocyanin concentra-
tion up to 300 hours. After this point, phycocyanin starts to decrease as a result of the nitrate
limitations.
Figure 6-22 Simulated and experimental biomass from A. platensis (Experimental data from Jing
2015) (Top) Simulated and experimental nitrate concentrations (Experimental data from
Jing 2015) (Bottom). The lines show the results from the simulation of the same experi-
mental conditions applied by Jing (2015).
- 66 -
Figure 6-23 Simulated and experimental phycocyanin concentration from A. platensis (Experimental
data from Jing 2015). The lines show the results from the simulation of the same experi-
mental conditions applied by Jing (2015).
- 67 -
7 Discussion
7.1 Influence of flow rate on biomass
An increase in flow rate results in an increase in the growth rate and final biomass of A. platensis
(Figure 6-4). This might be caused by the equilibrium between the negative effects of shear
damage and the positive influence of the flow rate increase on light availability and mass trans-
fer of CO2, with the positive influence being predominant.
Even if the cyanobacteria are exposed to higher shear stresses at 5 vvm, this exposure is inter-
mittent. Figure 6-2 shows that there are two zones with different 𝜀 values: one that ranges from
0 to 0.08 m2 s-3 and another that displays the bubble plume zone with higher values. Therefore,
cyanobacteria are exposed to an intermittent 𝜀 due to the transition between these zones. Since
Molina et al. have found better growth of Protoceratium reticulatum with intermittent rather
than continuous 𝜀 exposure (García Camacho et al. 2007), this might result in an advantage for
A. plantesis as well. In sum, at values up to 1.34 Pa in cultivations of A. platensis, the biochem-
ical process in the cells may be affected by turbulence but without any serious damage. Never-
theless, light availability and pH control play a more important role within this process, mini-
mizing the effects of the possible damage caused by the turbulence.
When a culture is light-limited, higher liquid velocities can help the cyanobacteria move more
quickly through the light gradients. Consequently, by improving the fluid velocities, a faster
transition between the dark and the light zone is facilitated (Degen et al. 2001; Trujillo et al.
2008). In other words, it is possible that at high flow rates there is more illumination available
per cell than at lower flow rates. This analysis may explain the better growth results found in
the reactor with 5 vvm than in the one with a volumetric flow rate of 1, in which higher liquid
velocities are predicted (Figure 6-1 and Figure 6-2).
The frequency, which is the inverse of the time cycle through the light and dark zones (Figure
6-5), together with the time fraction in the light zone, have been regarded as the two main factors
in the light increase per cell in cyanobacteria culture, which leads to better growth. This effect
has been demonstrated by several experiments with laboratory equipment that control the fre-
quency and light time fraction (i.e. tours photobioreactor (Pruvost et al. 2008)). However, it is
challenging to characterize the frequency and the light time fraction in bubble columns due to
their chaotic hydrodynamic behavior.
- 68 -
Luo et al. used Computer Automated Radioactive Particle Tracking (CARPT) to track the light
history of particles (Luo and Al-Dahhan 2004). This work found an enhancement in the light
intensity per cell with the increase in the flow rate. This results from high frequency 𝑓, coupled
with higher times in the light zone ∅. In sum, a greater frequency and time fraction in the light
zone can lead to better growth at a flow rate of 5 vvm, as the specific growth rate seems to
depend on the light available per cell.
In addition to better light usage at 5 vvm, high flow rates also have positive effects on the pH
(Figure 6-6) by maintaining it close to optimal, as discussed in more detail below. In cyanobac-
teria, after the bicarbonate has passed through the cell membrane, the bicarbonate is reduced by
the enzyme carbon anhydrase (Figure 7-1). As a result, CO2 is incorporated into the algal me-
tabolism and hydroxyl (OH-) is excreted into the medium. A one-to-one stoichiometric rela-
tionship between the formation of OH- and the removal of (HCO3-) by the blue green-algae has
been reported (Miller and Colman 1980). Therefore, due to the removal of bicarbonate, the pH
increases when the dissolved carbon dioxide is low (Uusitalo 1996).
Figure 7-1 Graphical representation of the medium alkalization mechanism.
Adding carbon dioxide to the medium can shift the bicarbonate equilibrium equation to the left,
but first it must be dissolved in the medium and converted from the gas phase to the liquid
phase. High kla values mean faster dissolved carbon equilibrium, which can generate positive
effects in medium alkalization.
The high pH in both cases (Figure 6-6 ) can be explained by the low carbon dioxide concentra-
tion used in those experiments (0.035%). The same trend was also found by Zeng et al., who
found increases in the culture pH as a result of a continuous shift in the bicarbonate equilibrium
system (Zeng et al. 2012) by atmospheric carbon dioxide . Furthermore, the different alkaliza-
tion rate (Figure 6-6) between the two flow rates can be explained by a higher mass transfer and
better growth in the cultivation at 5 vvm. Higher mass transfer leads to higher dissolved carbon
dioxide and a good growth rate generates faster bicarbonate consumption. These two conditions
may be the reason for low velocities of medium alkalization at high flow rates (5 vvm).In sum,
high flow rates favor biomass growth in cultivations which are light-limited and/or cultivated
- 69 -
in atmospheric carbon dioxide concentrations (0.035%). This results from better light usage and
from maintaining the pH close to optimal.
Although increasing the flow rates seems to have a positive effect on growth, some of the bot-
tlenecks in the cyanobacteria production in closed photobioreactors are the power consumption
necessary for mixing and mass transfer, as well as the high investment capital necessary for the
photobioreactor. Increasing the flow rate from 1 to 5 vvm represents an increase in the energy
from 75 W m-3 to 250 W m-3 (Norsker et al. 2011). The energy costs for mixing have a strong
influence on the economics of microalgal biomass production in photobioreactors. For these
reasons, different strategies have been proposed to maintain a constant flow rate while also
increasing the cyanobacteria circulation or mass transfer coefficient. For instance, adapting a
static mixer has been reported to increase the biomass productivity of chlorella by 37%. This
can be explained by shorter light/dark cycles, which result from adapting the static mixer (Wu
et al. 2010). Furthermore, the use of membranes to increase the mass transfer coefficient has
also been examined as a possible strategy to achieve these goals for algae mass growth and cost
efficiency. Last but not least, another strategy is the use of incremental increases in the flow
rates, which has also been reported to have positive effects in cyanobacteria cultivations (Zeng
et al. 2012)
7.2 Influence of carbon dioxide on biomass
During cultivation with the normal fraction of carbon dioxide in the air (0.035%), slow growth
and low final biomass were found due to the high pH. As already explained, this high pH is a
consequence of medium alkalinisation. However, by using 3% CO2 the pH decreases (see Fi-
gure 6-7), perhaps as a result of the high partial pressure (Figure 6-9). Although the growth in
this case is better than in the experiment at 0.035%, the pH is lower than the optimal pH reported
in A. platensis cultivations.
The primary source of inorganic carbon for A. platensis is the bicarbonate ion (HCO3-) (Cornet
et al. 1998). In the standard spirulina medium, the bicarbonate concentration in the medium is
approximately 9.8 g l-1. This concentration seems to be sufficient to support growth, but carbon
dioxide must be used to maintain the optimal pH. The modification of the bicarbonate/carbonate
equilibrium has an impact on the cyanobacteria pH, which can influence the cyanobacteria
growth rate, as seen below in Table 7-1:
- 70 -
Table 7-1 Experimental growth rates for different pH in Arthrospira platensis.
Carbon dioxide
Concentration pH µ (h-1)
3 % 8.5 0.0080
0.035 % 11 0.0055
0.8 % 9.3 0.0095
After further simulations, an optimal carbon dioxide concentration of 0.8% was chosen for sub-
sequent experiments, since this concentration leads to an optimal pH of approximately 9.3 In
practice, this concentration actually leads to a marginal growth increase compared to the exper-
iment in which 3 % CO2 was used (Figure 6-8). These results confirm that the simulation of the
CO2 partial pressure in the cultivation can be used to optimize it without the need for test ex-
periments and online measurements. The use of higher CO2 concentrations in the inlet leads to
further reductions in the pH, which cause a decrease in the growth rate and increase the carbon
dioxide waste. For example, concentrations of 6 % (v/v) carbon dioxide have been tested with
A. platensis by using a carbon-free medium, with decreases in the pH down to 7.5 and non-real
carbon dioxide biofixation (De Morais and Costa 2007). In conclusion, an optimal carbon di-
oxide concentration must be established in order maintain the optimal pH and carbon supply
but without waste of carbon dioxide. A mathematical model can be helpful for this purpose.
7.3 Influence of light intensity on biomass and nitrate consumption
Among the environmental factors affecting the growth rate of cyanobacteria, light is frequently
limited. Figure 6-10 and Figure 6-15 show a better growth rate and final biomass concentration
with the increase in the light intensity. As was expected, high photon flux density leads to rapid
production of ATP and NADPH, and therefore to faster metabolic pathway rates (Klanchui et
al. 2012). Consequently, faster growth also generates faster nutrient consumption. As nitrate
compositions are linked to the growth rate by the yield of consumption, faster nitrate consump-
tion is expected.
According to the model (Figure 6-15), nitrate depletion occurs after 100 hours in the cultivation
with 400 µmol m-2 s-1, whereas in the cultivation with 60 µmol m-2 s-1 some nitrate still remains
after 250 hours of cultivation. By using 600 µmol m-2 s-1 and an initial nitrate concentration of
0.9 g l-1, the limitation begins after 50 hours (Figure 6-16). Different nutrient concentrations
- 71 -
during cultivation can also lead to different cyanobacteria compositions. This is discussed be-
low in the section on phycocyanin formation and degradation.
7.4 Model fitting performance for biomass
The model fitting performance was tested against several culture conditions. The model was
able to confirm external literature data and predict the biomass growth curve of A. Platensis
after the variations in the flow rate, initial carbon dioxide concentration and Incident light in-
tensity on PBR surface up to 600 µmol m-2 s-1. Table 7-2 shows the main output in biomass
formation with the modifications of flow rates, carbon dioxide concentrations and light input,
as well as the model mechanisms that control these outputs. The proposed model (Equations 18
to 26) adequately describes the biomass production and phycocyanin formation.
All Monod half saturation constants, Ki, Kip, Kb, Kpc and Kn, as well as the maximum specific
growth rate µmax were validated. The light intensity mechanism in the active biomass equation
(Equation 23) 𝐼
𝐼+𝐾𝑖+𝐼2
𝐾𝑖𝑝
properly describes in correct way the influence of light. In order to use
the model in a large scale photobioreactor, the light input (I) in each time-step must be corre-
lated with the cyanobacteria trajectories and not average values along the radius as was done in
this work. The absorption coefficient Ea is affected by phycocyanin and chlorophyll A, and in
the simulation in this work described the phycocyanin changes over time. However, chlorophyll
A was assumed to be constant throughout the cultivation. The model’s predictive capability can
be improved by including these additional factors.
Although only the theoretical yield of consumption for nitrate yn/x, was validated, it can be as-
sumed that the others, for bicarbonate yb/x and phosphate yp/x, are correctly calculated. The the-
oretical yields of consumption to enable the biomass calculation help in the overall prediction
of these macronutrients over the course of time.
It is important to highlight that in batch cultivations the kla can decrease over time, as the
viscosity in the medium increases. An increase in the viscosity due to the production of exopol-
ysaccharides in A. platensis cultivation has been reported. Unfortunately, the model proposed
in this work assumed a constant kla during the cultivation.
After depletion of nutrients, especially nitrate, a change in the biomass composition strongly
affects the predictions. Glycogen accumulation and gradual exopolysaccharide increase must
be accounted in to the biomass formation model. In this work, this effect is introduced in the
- 72 -
terms ( 𝑍𝑝𝑐
𝑍𝑝𝑐+𝐾𝑝𝑐×
𝐾𝑛
𝑛+𝐾𝑛 ) in Equation 23. The term
𝐾𝑛
𝑛+𝐾𝑛 correctly described the effect on biomass
growth due to the accumulation of glycogen and EPS in the cell wall as a result of the nitrogen
depletion. However, if cells do not divide, growth stops when cells reach their maximum size.
This is described by the term 𝑍𝑝𝑐
𝑍𝑝𝑐+𝐾𝑝𝑐 in Equation 23.
Table 7-2 Final remarks on model fitting performance.
Parameter Impact on biomass Mechanism
Increase of flow rates
up to 5 vvm Increase
Generating more light
availability per cell
and helping to stabi-
lize the pH
Increase of carbon diox-
ide concentrations up to
3%
Increase Helping to stabilize
the pH
Incident light intensity
on PBR surface up to
600 µmol m-2 s-1
Increase Higher internal light
intensities
7.5 Phycocyanin production: biosynthesis, steady state and degradation
For biotechnological application, the formation of the putative product is of great importance.
Thus, the evaluation of the parameters that influence product formation is the main goal of the
present work. The phycocyanin mass fraction in A. platensis cells varies from 5 to 20 mg g-1,
with productivities ranging from 10 to 125 mg l-1 d-1 (Chen et al. 2013; Xie et al. 2015). In
phototrophic cultivations, the light intensity strongly influences the cell growth of cyanobacte-
ria and it also changes the levels of light-related molecules in photosynthetic systems. Changes
in the nutrient conditions (light, nitrate, etc.) can lead to three possible stages in the phycocyanin
biochemical pathways: biosynthesis, degradation and steady state.
Figure 6-13 shows that phycocyanin is biosynthesized in the cell, probably due to the low light
conditions. Light intensity is one the most significant factors that influences the light harvesting
complex (phycobilisomes). However, its role is not yet fully understood, but perhaps is a re-
sponse of the photoadaptation processes in order to reach a new steady state. Nonetheless, an
alteration of the photosynthetic units at low or high light intensities has been reported (Rubio
et al. 2003).
Biosynthesis occurred in the experiment with 60 µmol m-2 s-1, perhaps due to the low light
intensities. Two conditions have been reported that trigger phycocyanin synthesis in the cell:
low nitrate (Xie et al. 2013)) and/or low light conditions (Takano et al. 1995). It has been shown
- 73 -
that low light intensities benefit phycocyanin formation. Takano et al. found that the maximum
phycocyanin mass fraction from the cyanobacterium synechococcus sp was at 25 µmol m-2 s-1
(Takano et al. 1995). In addition, they found that phycocyanin content decreases when the light
intensity passes this limit. However, the precise values of low light or low nitrate are not given
for A. platensis. If we make a comparison to the cyanobacterium synechococcus sp, a light value
between 5 and 25 µmol m-2 s-1 can be expected as the range of values that trigger the metabolic
pathway in phycocyanin biosynthesis.
As was mentioned before, phycocyanin was biosynthesized in the cell between 60 hours and
180 hours. After 180 hours the phycocyanin production stopped and the level remained stable
until the end of the cultivation. As the model predicts (Figure 6-12), nitrate is not depleted during
the course of the cultivation at 60 µmol m-2 s-1. Consequently, nitrate limitation can be elimi-
nated as a possible cause of the cessation of phycocyanin production.
According to the simulations, after 50 hours the light inside the reactor is lower than 10 µmol
m-2 s-1 (Figure 6-11). In addition, simulations also confirm that after 180 hours of cultivation,
80% of the internal light in the reactor is lower than the compensation point (4.5 µmol m-2 s-1)
for A. platensis. This may be the reason for the cessation of phycocyanin production and, there-
fore, of the photoautotrophic biomass production in the experiments with low light intensity
(Figure 6-13).
Some researchers have found that phycocyanin is biosynthesized during the exponential growth
phase (Chen et al. 2013; Xie et al. 2015), while others have found an entirely steady state in the
phycocyanin mass fraction. However, As Figure 6-13 shows, the phycocyanin mass fraction
was biosynthesized even during the exponential phase in the cultivation at 60 µmol m-2 s-1.
Phycocyanin was also built up in the cell during the experiment with high light intensity (400
µmol m-2 s-1) (Figure 6-14). However, in this case, the reason may have been that formation was
stimulated when a low level of nitrate was reached. The explanation for this is that at a low
concentration of nitrate, the nitrogen must first be used to synthesize light harvesting molecules
(Xie et al. 2015). Similarly, Xie et al. also reported that a higher lutein content was obtained in
a fed batch culture with a relatively lower concentration of nitrogen (Xie et al. 2013). In addi-
tion, Csőgör et al. found the same trend in the formation of phycoerythrin by Porphyridium
purpureum; in their research the pigment concentration rises when the specific growth rate be-
comes lower (Csőgör et al. 2001). This suggests that by maintaining a low but non-limiting
level of nitrogen, the accumulation of phycocyanin is enhanced.
- 74 -
Nevertheless, the phycocyanin production inside the cell ceased after 100 hours of cultivation
and the concentration began to decrease (Figure 6-14). Under complete nitrate limitation condi-
tions, it has been reported that phycocyanin is degraded. According to simulations made with
the model at 400 µmol m-2 s-1, nitrate should be entirely depleted and phycocyanin decline
should occur.
In experiments with the cyanobacterium synechococcus, Lau et al. found a loss of spectropho-
tometrically measurable phycocyanin, which began soon after the resuspension in a nitrate-free
medium (Lau et al. 1977). During nitrogen starvation, cyanobacteria may consume internal
stores of nitrogen to prolong their growth. In support of this, previous studies have shown that
glycogen is accumulated during nitrogen starvation. For example, Joseph et al. found that Syn-
echocystis sp. stores glycogen and degrades nitrogen-rich phycobilisomes, which results in the
loss of the pigment phycocyanin, a condition referred to as bleaching (Joseph et al. 2014).
Moreover, Hasunuma et al. also found an increase in internal glycogen from 10% to 60% and
a reduction in protein content from 42% to 15% of dry weight after 72 hours (Hasunuma et al.
2013). Additionally, they discovered that the glycogen produced during the depletion is bio-
synthesized with carbon atoms from proteins rather than CO2. Furthermore, Cornet et al. found
the same trend, confirming that as soon as nitrate is exhausted, phycocyanin begins to degrade
and is used to synthesize energy storage products such as glycogen. The size of cells continues
to increase but they no longer divide, which explains the continued increase in biomass (Cornet
et al. 1998).
The degradation of phycocyanin after nitrate limitation explains the results in the experiment at
400 µmol m-2 s-1, in which the biomass production was accelerated (Figure 6-15) and the phy-
cocyanin declined (Figure 6-14). In addition, in the fed batch and control experiment, phycocy-
anin degradation (Figure 6-18) took place due to the nitrate-limitation conditions, as predicted.
This degradation can explain the higher biomass in the control experiment (between 50 and 200
hours) compared to the experiment with nitrate addition (Figure 6-17). In addition, the slightly
lower biomass concentration (Figure 6-17) in the fed batch was probably also a result of the
higher phycocyanin concentration (Figure 6-18). According to (Cornet et al. 1998), the higher
the phycocyanin mass fraction, the higher the light absorption, which consequently leads to
more light being highly attenuated.
With the nitrate addition, the phycocyanin mass fraction was expected to remain at least con-
stant throughout the cultivation. However, the phycocyanin decreased after the third addition
(76 hours), but at a slower rate than in the control experiment (Figure 6-18). Based on the model,
- 75 -
bicarbonate limitations are proposed to be the reason for this decrease. This is discussed in more
detail in the next section. However, in the nitrate fed batch experiment, the phycocyanin mass
fraction and therefore the productivity remained at a higher concentration compared to the ex-
periment without nitrate addition (Figure 6-18).
7.6 Phycocyanin kinetic model
The wide range of phycocyanin productivity in the literature and in this work is explained by
the different experimental conditions. A mathematical model that comprises growth and phy-
cocyanin biosynthesis can explain the conditions that lead to these productivity levels. How-
ever, no kinetic model for phycocyanin biosynthesis currently exists.
Advanced structural models consider that the biomass can change its composition during the
time of cultivation as a result of changes in substrates. In particular, the phycocyanin mass
fraction 𝑧𝑝𝑐 has been shown in this work not to be constant, instead changing as a consequence
of the metabolic pathway shift. Structural models describe not only biomass kinetics, but also,
in particular, the product formation kinetics for transient operation, using a small set of param-
eters which often have a biological meaning. The semi-empirical kinetic law for phycocyanin
mass fraction (Equation 28) was used to simulate its formation.
Equation 28: 𝑑𝑧𝑝𝑐
𝑑𝑡= 𝑅𝑝𝑐 × (
Kli
𝐼+Kli − (
𝐼
𝐼+𝐾𝑙𝑖+
𝐾𝑛
𝑛+𝐾𝑛+
𝐾𝑏
𝑏+𝐾𝑏) ) × 𝑧𝑝𝑐
This kinetic model was linked to the core model and solved simultaneously. In this equation,
the maximum phycocyanin formation rate Rpc (0.02 mg g-1 h-1) is negatively affected by the
following factors:
1. High and low light intensities
2. Nitrate deprivation
3. Bicarbonate deprivation
The first two effects were verified in this work. By cultivating in high light intensities (Figure
6-20) (400-600 µmol m-2 s-1), this mechanism (𝑲𝒍𝒊
𝑰+𝑲𝒍𝒊) is able to capture photoadaptation pro-
cesses due to the high illumination. The positive effects of low light intensities are modelled
through this law (𝑰
𝑰+𝑲𝒍𝒊). The nitrate mechanism
𝑲𝒏
𝒏+𝑲𝒏 describes the well-documented phenom-
enon involving the degradation of phycocyanin due to nitrate limitations.
Bicarbonate results from the simulations performed with the same conditions as in the experi-
ments (Figure 7-2) show bicarbonate depletion before 100 hours of cultivation, which matches
- 76 -
the time at which phycocyanin began to decrease in the fed batch experiment. These results
came from the Equation 19, which includes the theoretical bicarbonate yield.
This work includes the depletion of carbon in the mechanisms that negatively affect the phy-
cocyanin mass fraction (Equation 28). It is important to highlight that this work is the first to
describe this phenomenon quantitatively. Further validation of the bicarbonate in the medium
is necessary to draw final conclusions. However, this is a first insight into how bicarbonate also
affects phycocyanin formation.
Figure 7-2 Simulated bicarbonate concentrations in the nitrate fed batch experiment. The line shows
the results from the simulation of the following conditions: 1.4 % carbon dioxide, 1 vvm,
30°C, which corresponds to the same experimental conditions implement in the PSM cul-
tivation
7.7 Exopolysaccharide production
Production of exocellular polysaccharides by cyanobacteria is known to respond to changes in
several external factors, such as nitrogen concentration and irradiance. The information in the
literature about the effect of nitrate on exopolysaccharide production is ambiguous. Some re-
searchers have described nitrogen starvation as a condition that enhances EPS synthesis, prob-
ably because this contributes to the increase in the C/N ratio, thus promoting the incorporation
- 77 -
of carbon into polymers. Meanwhile, others have reported that the presence of an abundant
nitrogen source in the culture medium resulted in an increase in EPS synthesis, probably due to
the lower energy requirement necessary for the assimilation of combined nitrogen compared
with the energy needed for nitrogen fixation (Pereira et al. 2009).
In addition, it has been shown that exopolysaccharides can be delivered as result of an overflow
in metabolism (Staats et al. 2000), which generates a drain of the excess of ATP (Cogne et al.
2003) by the exopolysaccharides. For example, (Abd El Baky et al. 2014) found the best ex-
opolysaccharide production at initial nitrate concentrations between 0.2 g l-1 to 0.5 g l-1. The
nitrate addition experiment shows an incremental increase in EPS at the end of the cultivation
(Figure 6-19) and, in this case, the rise in EPS corresponds to the nitrate depletion (Figure 6-17).
However, in the control experiment, in which the nitrate depletion occurred after 50 hours, there
was no increase in EPS formation. In addition, the EPS mass fraction remains lower than the
level in the nitrate addition experiment (Figure 6-19). These findings show that nitrate limitation
is not the only triggering factor in EPS formation.
A possible explanation for this behavior it is that not limitations not only of nitrate are necessary
to trigger EPS formation, but also of another macro-element (e.g. phosphate) or micro-element.
Phosphate predictions using the model show low levels of phosphate after 200 hours (Figure
7-3). It has also been reported that phosphate starvation or low levels of phosphate induced an
increase in EPS production. However, in C. capsulata the absence of phosphate had no signif-
icant effect, and in Anabaena spp. and Phormidium sp., it significantly decreased EPS produc-
tion (Nicolaus et al., 1999). Phosphorus starvation may also induce carbohydrate accumulation
over protein accumulation. In the case of A. platensis, carbohydrate accumulation was reported
to amount to approximately 63% of cell dry weight following phosphate starvation. However,
in this work, phosphate limitations as a possible triggering factor for EPS cannot be considered
a final conclusion, as the phosphate predictions have not yet been validated. Finally, this work
has demonstrated that feeding nitrate into the culture can help yield reasonable productivity of
EPS (32 mg l-1 d-1)
- 78 -
Figure 7-3 Simulated phosphate concentrations in different culture conditions The lines show the
results from the simulation of the following conditions: 1.4 % carbon dioxide, 1 vvm,
30°C, which corresponds to the same experimental conditions implement in the PSM cul-
tivation
- 79 -
8 Possible experimental errors
For the experimental work, the initialization with pre-cultures with different biomass composi-
tions, e.g. phycocyanin concentration, can lead to small changes in the biomass growth curves.
Therefore, a rigorous protocol must be established in order to produce a pre-culture with the
same features, even if the experiments are performed at different periods of time.
As a result of the sampling process, there are changes in the volume of the culture. This outcome
may create different hydrodynamic conditions that could also affect growth. Although all rota-
meters and light bulbs were calibrated before use, the precision of such systems is not optimal,
so there may have been an error in the flow rate or in the incident light intensity on PBR surface
adjustment. Additionally, at the end of the cultivations a cyanobacteria aggregation generated
difficulties in obtaining perfectly homogenous samples and this may have led to errors in the
analytical measurements. After a biomass concentration of 4 g l-1, biomass aggregations and
cell growth in the wall in the current set-up must be resolved in order to obtain a perfectly
homogenous sample.
Finally, human errors in quantification of dry biomass, phycocyanin and exopolysaccharides
may have occurred during handling of the samples. However, all precautions were taken for the
biomass weight measurements and sample preparation in the analysis of phycocyanin.
- 80 -
9 Model limitations
The semi-empirical model proposed in this work is based on Monod type kinetics, which is
based on empirical constants. Some of the assumed constants come from the experiments con-
ducted within this work, while others are deduced from other literature. For example, the yield
of consumptions is derived from theoretical stoichiometric equations for A. platensis and Mich-
aelis-Menten constants were obtained from other studies. In addition, the mass transfer coeffi-
cient was calculated with an empirical correlation and was assumed to be constant during the
course of the cultivation. However, it is not completely precise, as the viscosity increased with
the growth in exopolysaccharide production and, therefore, the mass transfer decreased during
the cultivation.
Determination of parameters for models taking into account multiple factors may not be easy
because it is difficult to simulate co-limitation conditions (e.g. experimental design and setup).
Furthermore, due to the many parameters (10 empirical parameters in this work) that must be
fitted with experimental data, such models often result in overfitting issues. Complex models
with many parameters often suffer from overfitting because they are too specific or sensitive to
the dataset used to develop the model. Even so, the model was able to predict the growth curve
of A. Platensis under different culture conditions (section 6.2).
In this work, the kinetic mechanism for product formation was validated for nitrate over time,
while other medium components were addressed in a largely speculative way in this mechanism
as possible triggering agents in the biosynthesis and degradation of exopolysaccharides and
phycocyanin. However, further bicarbonate and phosphate validations are necessary to verify
the assumptions made in the mechanism.
In sum, due to its semi-empirical nature, the extrapolation of the model to experimental condi-
tions other than those validated in this work must be performed with caution. However, know-
ing the limitations, the model can help predict and understand the behavior of batch cultivation
of A. platensis under various culture conditions.
- 81 -
10 Final remarks and further study
In batches, the rate of overproduction of metabolites by cyanobacteria is limited or activated by
the depletion of required substrates or by the accumulation of metabolic products and inhibitors.
In addition, different nutrient concentrations during cultivation can lead to different cyanobac-
teria compositions. In other words, controlling nutrient conditions can enhance the production
of key compounds by cyanobacteria. Therefore, it is essential to identify the parameters that
have a significant impact on product formation and to create a mathematical model that can
assist the investigation, optimization and increase of A. platensis growth and phycocyanin and
exopolysaccharide production in batch cultivation. However, this requires not only having a
complete understanding of the mechanisms involved in the limiting process, but also studying
them at different levels (metabolism and physiology).
This work has shown that the use of mathematical models in cyanobacteria cultures can help
interpret experimental results and to predict future behaviors after modifying the culture condi-
tions. In particular, this research has demonstrated that controlling nutrient concentrations (e.g.
nitrate) is a viable strategy for improving production, in this case of phycocyanin and exopoly-
saccharides.
The effect of nitrate concentration on the growth kinetics of A. platensis and its phycocyanin
content was quantitatively interpreted in this work. This was then used to propose a feeding
approach in order to keep this molecule constant during cultivation. Furthermore, the mathe-
matical model was able to predict the nitrate consumption in A. platensis cultivations. Under a
light intensity of 600 µmol m-2 s-1, rapid growth leads to nitrate depletion after 50 hours of
cultivation and this led to the observation of rapid phycocyanin degradation. Consequently, a
nitrate fed batch strategy was proposed for the purpose of lowering the phycocyanin degrada-
tion. Nitrate additions during the cultivation help to keep constant this molecule until new
macro-element limitation appear. According to the model, bicarbonate is this limitation. There-
fore, a kinetic law for phycocyanin formation which includes this phenomenon was established.
The effect of nitrate on exopolysaccharide production was also addressed, and in a largely spec-
ulative way, low phosphate levels were proposed as a potential triggering mechanism is EPS
formation. However, further experimental measurements are required with regard to phosphate
and bicarbonate consumption and its influence on product formation.
Finally, an approach based on comprehensive mechanistic relationships could help us under-
stand how cells interact with their culture medium over time with regard to culture behavior,
- 82 -
dynamic approaches being more appropriate for developing an in silico platform. In the future
we will need to start producing large-scale kinetic models. This work thus paves the way toward
an in silico platform making it possible to assess the performance of different culture media and
fed-batch strategies. As a first approach, the nitrate fed batch strategy proposed in the mathe-
matical model in this work leads to a phycocyanin productivity of 38 mg l-1 d-1 and an exopol-
ysaccharide productivity of 33 mg l-1 d-1.
- 83 -
11 Annex
function process2 clear all, clc, close all global umax A Bi k Kn Ynx Zpc Zch R L Is de KHCO Yco H kla pc k1 k2 kw c fc
Kpc Rpc Ipc Kni fa Rpcd Ypx kip pc2 klao m i inini1 %% % _*%%%%%%%%%%%%%%%%%%parameters which can be modified%%%%%%%%%%%%%%*_ Is1=[600,400,70,600]; %set light intensity (µmol/m2*s-1) for these yields
between (10-120) 46 cornet klao=29; % Flowrate=90; %flow rate (l/h) R1=[0.025, 0.025, 0.025, 0.025]; %reactor radius (m) P=101325; % pascal (Absolute Total Working Pressure) yc1=[1.4,1.4,1.4,1.4]; ph=[9,10.5,9.5,9]; u=0.0693 %u=0.0923; 0.07625 umax1=[u,u,u, u]; fa1=[1,1,1, 1]; inibi1=[0.6,0.66,0.3, 0.60]; kti=[200,200,200,200]; %178 Ynx1=[0.50,0.50,0.50,0.50]; Ipc1=[0.10, 0.06, 0.04, 0.09]; %0.065 ka1=[3,3,3,3]; fc1=[1,1,1,1]; %factor 20% more light due to mixing inini1=[0.9,1.8,1.8,0.9]; for m=1:length(yc1) R=R1(1,m); kla=ka1(1,m); %overall mass transfer coeficient (h^(-1)) 6-7 2 fc=fc1(1,m); yc=yc1(1,m); % Percentage of % CO2 in feed gas (%) Is=Is1(1,m); umax=umax1(1,m); fa=fa1(1,m); k=kti(1,m); Ipc=Ipc1(1,m); H=3412; %Hery coeficient at 25°c (Pa*m3/mol) (30.04 bar*L/mol) 3412
(Pa*m3/mol) at 25°c %%%%%%initial cocentrations Spirulina Medium Concentra-
tion%%%%%%%%%%%(kg/m3) inib=inibi1(1,m); %biomass (kg/mt3) inini=inini1(1,m); %Nitrate (kg/mt3) 1.3 % inisul=0.3; %sulfate (kg/mt3) 0.3 inipho=0.2; %phosphate (kg/mt3) 0.2 bic=9.88; %%Bicarbonate (kg/mt3) 7.2 carbon=1.7; %%carbonate (kg/mt3) 1.7 Tsim=320; %%%simulation time (h) %fc=1.0; %factor 20% more light due to mixing %% % _*%%%%%%%%%%%%%%%%%%parameters which can be modified_They are specifc for % ever microalgae( i.e Arthrospira platensis) %%%%%%%%%%%%%%*_ %maximuspecifgrowth(h-1)
%k=3; %MichaeliseMenten constant of light intensity umol/m2s-1 %%%%%%%%%%%% this yields are assuming 90% of active biomass 10% EPS 100 %%%%%%%%%%%% umol/m2s-1 Kn=4*10^-3 ; %MichaeliseMenten constant of Nitrate (kg NO3/m3) Ynx=Ynx1(1,m); %Yield of Nitrate (kg NO3/kg total biomas (active+EPS) mod-
ified form 0.4 to 0.9 kip=800; % Ks=2.5*10^-4 ; %MichaeliseMenten constant of Sulfate(kg SO3/m3)
- 84 -
% Ysx=0.024; %Yield of Sulfate(kg SO3/kg total biomas (ac-
tive+EPS) % Kp=2.7*10^-4 ; %MichaeliseMenten constant of phosphate (kg PO3/m3) Ypx=0.024; %Yield of phosphate(kg PO3/kg total biomas (ac-
tive+EPS) Yco=2.8; %Yield of total carbon (kg /m3) (kg carbon/m3) (1.47-4.4)
(2.571) KHCO=8*10^-3; %MichaeliseMenten constant of total carbon Kpc=0.12; %MichaeliseMenten constant of phyco (kg/m3) Rpc=0.02; %h-1 %Rpc=0.02; Rpcd=0.000;
%%%%%%%%%%%%%%%%%%%%%product formation yield by cornet%%%%%%%%%%%%%%%%% % Zpr=0.5; %kgpr/kgbiomas %protein formation %Zpc=0.13; %kgpc/kgbiomas %phycocyanin %kgpc/kgbiomas %phycocyanin Zch=0.009; %kgCLh/kgbiomas %Chlorophyll a 0.0089-0.015 % %%%%%%%%%%species equlibrium constants for pH calculations %%%%%%%%%% k1=10^-6.381; k2=10^-10.37; kw=10^-14; options = optimset('LargeScale','off','Display','off','TolFun',1e-16); %% %%%%%%%%%%%load experimental data %ex(:,:)= xlsread('fabiandata.xlsx'); % ex(:,:)= xlsread('newdata.xlsx'); % %ex1(:,:)= xlsread('newdata.xlsx'); % ex1(:,:)= xlsread('newdata2.xlsx'); ex1(:,:)= xlsread('Fabian20162x.xlsx'); ex(:,:)= xlsread('new3data.xlsx'); %% %%%%%%%one parametre modification sensitive analysis % kla1=[2.5,12,17,28]; % for m=1:length(kla1) % % kla=kla1(1,m); %overall mass transfer coeficient (h^(-1)) 6-7 27 % % end %%%%%%%%%%%solving the model%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% tspam=linspace(0,Tsim,100); x4_0 = zeros(9,1); x4_0(1) = inib; x4_0(4) = inini; % x4_0(4) = inisul; x4_0(9) = inipho; de=x4_0(1); x4_0(5) = x4_0(1)*Zch; %chla (kg/mt3) x4_0(3) = Ipc; %phico (kg/mt3) %x4_0(5) = Ipc; %phico (kg/mt3) % x4_0(8) = x4_0(1)*Zpr; %proteins (kg/mt3) x4_0(2) = x4_0(1); %biomass+glucogen (kg/mt3) pc=P*(yc/100); %partial presure yce=0.035; %exit pc2=P*(yce/100); %exit %disol=(((pc/(H))*44)/1000); x4_0(7) = (bic)*fa; %total disolved carbon (kg/mt3) x4_0(6) = (((pc2/(H))*44)/1000); x4_0(8) = 0.986; x4_0(10) = 0.896;
- 85 -
x4_0(11) = 0.811; x4_0(12) = 1.227; %%%%%%%%%%%%%%%solving%pH%model%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% c=pc/H; %mol/m3 xo = [1; 1]; % Make a starting guess at the solution [y]=fsolve(@pHmodel,xo,options); pH=-log(y(1)); %pH wil be calculated as fuction of bicarbonate (117
mol/m3)(pH=9.2) %%%%%%%%%%%%% [t_traj, x_traj] = ode15s(@Cinetica,tspam,x4_0);
s1(:,:,m)=x_traj; %%%%pH calculation
% L1(:,:)=x_traj'; % %%%%%%%%%%%%%%%solvingPH when co2 model is active%%%%%%%%%%%%%%%%%%%%%%%%
end
%% %%%%%%%%%%%%%%%%%%%Data extraction to plot %%%%%%%%%%%%%%%%%%%%%% for m=1:length(yc1) a=(s1(:,7,m)); a1=(a*1000)/60; %%bicrbonate b=s1(:,6,m); b1=(b*1000)/44; for i=1:length(b1) pkac1=5.5; pH(i,m)=pkac1+log10(a1(i)/b1(i)); end end
for i=1:length(x_traj)
for m=1:length(yc1)
%if s1(i,3,m)>=1
A11=linspace(0.0001,R,1000); A1=A11/R; alfa(i,:,m)=((A*(s1(i,3,m)+0.009))/(A*(s1(i,3,m)+0.009)+Bi))^(1/2); gama(i,:,m)=(A*(s1(i,3,m)+0.009)+Bi)*alfa(i,:,m)*s1(i,2,m)*R; per(i,:,m)=gama(i,:,m)*A1; TO=1./A1; al(i,:,m)=((2*cosh(per(i,:,m)))); bp(i,:,m)=(cosh(gama(i,:,m))+alfa(i,:,m)*sinh(gama(i,:,m))); AK(i,:,m)=al(i,:,m)/bp(i,:,m); IM(i,:,m)=(Is1(1,m)*TO).*AK(i,:,m); Ir(i,:,m)=fc*mean(IM(i,:,m));
% else % zt(:,1)=A.*x_traj(:,2,m); % w(:,1,m)=Is./zt(:,2,m); % It(:,1,m)=1-exp(-zt(:,1,m));
- 86 -
% Ir(:,1,m)=fc*w(:,1).*It(:,1,m); % end
end end
for i=1:length(tspam) t=tspam'; pr=s1(i,:,1)'; y= feval(@Cinetica,t(i), pr); y1=y'; y2(i,:)=y1; end %% %%%%Ploting comands%%%%%%%%%%%%%%%%%%%%%%%
figure(1); subplot(2,1,1) a2=plot(t_traj,s1(:,2,4)) set(a2,'LineStyle','-' ,'LineWidth',1,'Marker','None','MarkerSize',8) set(a2,'Color',[0,0,0]) hold on
a1=plot((ex1(:,1)),ex1(:,5)) set(a1,'LineStyle','None','LineWidth',0.5,'Marker','diamond','Mark-
erSize',4) set(a1,'Color',[0,0,0]) ylabel('Biomass (g L^{-1})','fontsize',14) xlabel('Time (hours)','fontsize',14) % a1=plot((ex(:,3).*24),ex(:,4)) % set(a1,'LineStyle','None','LineWidth',0.5,'Marker','o','MarkerSize',4) % set(a1,'Color',[0,0,0]) hold off % set(a1,'LineStyle','None','LineWidth',0.5,'Marker','square','Mark-
erSize',4) % set(a1,'Color',[0,0,0]) %set(a9,'YColor',[0,0,0]) ylim([0 10]); xlim([0 270])
% hold off
% h = legend('Fed-batch-strategy','Fed-batch-strategy',0); % legend('boxoff') % hold off % xlabel('input'); % text(0,11,'A', 'Interpreter', 'latex', 'fontsize',14);
%figure(2) subplot(2,1,2)
- 87 -
a1=plot((ex1(:,1)),ex1(:,6)) set(a1,'LineStyle','None','LineWidth',0.5,'Marker','diamond','Mark-
erSize',4) set(a1,'Color',[0,0,0]) hold on ylim([0 1.5]); xlim([0 270]); ylabel('Nitrate (g L^{-1})','fontsize',14) xlabel('Time (hours)','fontsize',14) a2=plot(t_traj,s1(:,4,4)) set(a2,'LineStyle','-' ,'LineWidth',1,'Marker','None','MarkerSize',8) set(a2,'Color',[0,0,0]) ylim([0 2]); xlim([0 270]); hold off
figure (6)
a10=plot(t_traj,(s1(:,3,4)*1000)) ylabel('Phycocyanin (mg g^{-1})','fontsize',14) xlabel('Time (hours)','fontsize',14) set(a10,'LineStyle','-.','LineWidth',1,'Marker','None','MarkerSize',8) set(a10,'Color',[0,0,0]) ylim([0 130]); xlim([0 270]);
hold on
% a4=plot((ex(:,3).*24),ex(:,5)*10) % set(a4,'LineStyle','None','LineWidth',0.5,'Marker','o','MarkerSize',5)
%3% % set(a4,'Color',[0,0,0]) a1=plot((ex1(:,1)),ex1(:,7)*10); set(a1,'LineStyle','None','LineWidth',0.5,'Marker','diamond','Mark-
erSize',4); set(a1,'Color',[0,0,0]) % ylabel('Phycocyanin (mg g^{-1})','fontsize',14)
hold off % a1=plot(t_traj,s1(:,7,1)); % ylabel('Bicarbonate (g L^{-1})','fontsize',14) % xlabel('Time (hours)','fontsize',14) % set(a1,'LineStyle','-','LineWidth',1,'Marker','None','MarkerSize',8) % set(a1,'Color',[0,0,0]) % %set(a9,'YColor',[0,0,0]) % ylim([0 10]); % xlim([0 320]);
% figure(3);
a1=plot(t_traj,Ir(:,1,1))
- 88 -
ylabel('light µmol m^{-2} s^{-1}','fontsize',14) xlabel('Time (hours)','fontsize',14) %set(a9,'LineStyle','None','LineWidth',2,'Marker','*','MarkerSize',8) set(a1,'Color',[0,0,0]) set(a1,'LineStyle','-','LineWidth',1,'Marker','None','MarkerSize',8) hold on a1=plot(t_traj,Ir(:,1,2)) ylabel('light µmol m^{-2} s^{-1}','fontsize',14) xlabel('Time (hours)','fontsize',14) %set(a9,'LineStyle','None','LineWidth',2,'Marker','*','MarkerSize',8) set(a1,'Color',[0,0,0]) set(a1,'LineStyle','--','LineWidth',1,'Marker','None','MarkerSize',8) a1=plot(t_traj,Ir(:,1,4)) ylabel('light µmol m^{-2} s^{-1}','fontsize',14) xlabel('Time (hours)','fontsize',14) %set(a9,'LineStyle','None','LineWidth',2,'Marker','*','MarkerSize',8) set(a1,'Color',[0,0,0]) set(a1,'LineStyle','-.','LineWidth',1,'Marker','None','MarkerSize',8) %set(a9,'YColor',[0,0,0]) hold off ylim([0 1000]); xlim([0 270]); % hold on % a2=plot(t_traj,Ir(:,1,2)) % set(a2,'Color',[0,0,0]) % set(a2,'LineStyle','--','LineWidth',1,'Marker','None','MarkerSize',8) % hold off % h = legend('Fed-batch-strategy',0); % legend('boxoff')
figure (7) a1=plot(t_traj,s1(:,7,2)); ylabel('Bicarbonate (g L^{-1})','fontsize',14) xlabel('Time (hours)','fontsize',14) set(a1,'LineStyle','--','LineWidth',1,'Marker','None','MarkerSize',8) set(a1,'Color',[0,0,0]) hold on a1=plot(t_traj,s1(:,7,4)); ylabel('Bicarbonate (g L^{-1})','fontsize',14) xlabel('Time (hours)','fontsize',14) set(a1,'LineStyle','-.','LineWidth',1,'Marker','None','MarkerSize',8) set(a1,'Color',[0,0,0]) a1=plot(t_traj,s1(:,7,1)); ylabel('Bicarbonate (g L^{-1})','fontsize',14) xlabel('Time (hours)','fontsize',14) set(a1,'LineStyle','-','LineWidth',1,'Marker','None','MarkerSize',8) set(a1,'Color',[0,0,0]) %set(a9,'YColor',[0,0,0]) ylim([0 10]); xlim([0 270]); hold off
figure(10) a1=plot(t_traj,s1(:,9,1)); ylabel('Phosphate (g/l)','fontsize',14) xlabel('Time (hours)','fontsize',14) set(a1,'LineStyle','-','LineWidth',1,'Marker','None','MarkerSize',8) set(a1,'Color',[0,0,0]) %set(a9,'YColor',[0,0,0])
- 89 -
ylim([0 0.2]); xlim([0 270]);
figure (9);
a1=plot(t_traj,pH(:,1)) ylabel('pH','fontsize',14) xlabel('Time (hours)','fontsize',14) set(a1,'LineStyle','-' ,'LineWidth',1,'Marker','None','MarkerSize',8) set(a1,'Color',[0,0,0]) %set(a9,'YColor',[0,0,0]) ylim([2 10]); xlim([0 320]); hold on
figure (10) subplot(2,1,1) a1=plot((ex1(:,1)),ex1(:,9)*10); set(a1,'LineStyle','None','LineWidth',0.5,'Marker','square','Mark-
erSize',4); ylabel('Exopolysaccharides (mg g^{-1})','fontsize',14) %set(a9,'YColor',[0,0,0]) ylim([0 110]); xlim([0 240]);
hold on a1=plot((ex1(:,1)),ex1(:,8)*10); set(a1,'LineStyle','None','LineWidth',0.5,'Marker','diamond','Mark-
erSize',4); set(a1,'Color',[0,0,0]) ylabel('Exopolysaccharides (mg g^{-1})','fontsize',14) ylim([0 120]); xlim([0 270]); hold off % a1=plot(t_traj,s1(:,7,1)); % ylabel('Bicarbonate (g L^{-1})','fontsize',14) % xlabel('Time (hours)','fontsize',14) % set(a1,'LineStyle','-','LineWidth',1,'Marker','None','MarkerSize',8) % set(a1,'Color',[0,0,0]) % %set(a9,'YColor',[0,0,0]) % ylim([0 10]); % xlim([0 320]);
subplot(2,1,2) a1=plot(t_traj(1:9),s1(1:9,4,1)); set(a1,'LineStyle','-','LineWidth',1,'Marker','None','MarkerSize',8) set(a1,'Color',[0,0,0]) hold on a2=plot(t_traj(9:16),s1(9:16,8,1)); set(a2,'LineStyle','-','LineWidth',1,'Marker','None','MarkerSize',8) set(a2,'Color',[0,0,0]) % ylabel('Nitrate g L^{-1}','fontsize',14) % xlabel('Time (hours)','fontsize',14) % set(a2,'LineStyle','-','LineWidth',1,'Marker','None','MarkerSize',8) % set(a2,'Color',[0,0,0]) a3=plot(t_traj(16:24),s1(16:24,10,1)); ylabel('Nitrate (g L^{-1})','fontsize',14) xlabel('Time (hours)','fontsize',14) set(a3,'LineStyle','-','LineWidth',1,'Marker','None','MarkerSize',8) set(a3,'Color',[0,0,0]) a4=plot(t_traj(24:31),s1(24:31,11,1));
- 90 -
set(a4,'LineStyle','-','LineWidth',1,'Marker','None','MarkerSize',8) set(a4,'Color',[0,0,0]) a5=plot(t_traj(31:100),s1(31:100,12,1)); set(a5,'LineStyle','-','LineWidth',1,'Marker','None','MarkerSize',8) set(a5,'Color',[0,0,0]) %set(a9,'YColor',[0,0,0]) a1=plot((ex1(:,1)),ex1(:,3)) set(a1,'LineStyle','None','LineWidth',0.5,'Marker','square','MarkerSize',4) ylim([0 2]); xlim([0 240]); a1=plot((ex1(:,1)),ex1(:,6)) set(a1,'LineStyle','None','LineWidth',0.5,'Marker','diamond','Mark-
erSize',4) set(a1,'Color',[0,0,0]) ylim([0 1.5]); xlim([0 270]);
hold off
figure(11) a1=plot(t_traj,s1(:,9,1)); ylabel('Phosphate (g/l)','fontsize',14) xlabel('Time (hours)','fontsize',14) set(a1,'LineStyle','-','LineWidth',1,'Marker','None','MarkerSize',8) set(a1,'Color',[0,0,0]) hold on a1=plot(t_traj,s1(:,9,2)); set(a1,'LineStyle','--','LineWidth',1,'Marker','None','MarkerSize',8) set(a1,'Color',[0,0,0])
a1=plot(t_traj,s1(:,9,4)); set(a1,'LineStyle','-.','LineWidth',1,'Marker','None','MarkerSize',8) set(a1,'Color',[0,0,0])
hold off %set(a9,'YColor',[0,0,0]) ylim([0 0.2]); xlim([0 270]); %% return %% function [f] = Cinetica(t,x) global umax A Bi k Kn Ynx Zch Zpc R Is de Yco KHCO H kla pc fc Kpc Rpc Ipc
Kni kli fa Rpcd Ypx kip P pc2 yce klao m inini1 f = zeros(12,1); %variables %kli=12.5; X=x(1); %biomass without glycogen (g/l) XT= x(2); %biomass+glycogen(g/l)
if m==1 %if t<80 if t<=28 N= x(4); %Nitrate (g/l) else if t<=52 N=x(8); else if t<=76 N=x(10);
- 91 -
else if t<=76 N=x(11); else N=x(12); end end end end else N= x(4) end
Ch=x(5); %chlorophyll (g/l) Pc= x(3); %phyco (gphyco/gbiomass) %Pc=Pcg*X; % Pr= x(8); %Protein (g/l) Dis=x(6); B=x(7); %bicarbonate (g/l)
%%%%%%%%%%%%viscosity and microalgaemovmentproblmes%%%%%%%%%%%%%%%%%%%
% if t>=139 % fc=0.20; % else % if t>=118 % fc= 1; % else % % fc=fc; % end % end %end %end
%%%%%%%%%%%%%%%%%%%%%%%%%% % if N<0.1; % A=7300; %extinction or absorption coeficient m2/kg % Bi=200; % else % A=7300; %extinction or absorption coeficient m2/kg % Bi=200; % end
A=1300; %extinction or absorption coeficient m2/kg Bi=200;
% % if N<0.1; % A=2200; %extinction or absorption coeficient m2/kg % Bi=200; %scatering coeficient m2/kg % else % A=1800; %extinction or absorption coeficient m2/kg % Bi=730; %scatering coeficient m2/kg % end
- 92 -
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% if XT>1 A11=linspace(0.0001,R,1000); A1=A11/R; alfa=((A*(Pc+0.009))/((A*(Pc+0.009))+Bi))^(1/2); gama=((A*(Pc+0.009))+Bi)*alfa*XT*R; per=gama*A1; TO=1./A1; al=((2*cosh(per))); bp=(cosh(gama)+alfa*sinh(gama)); AK=al/bp; IM=((Is*TO).*AK); I1=fc*mean(IM);
%%%%%%%%%%%%beer lambert else AY=30; A11=linspace(0.0001,R,1000); IM =Is*exp(-AY*XT*A11); I1=fc*mean(IM); I=I1; end
if I1<6; I=2; else I=I1; end
% end
kli=90; %%%%%%kinectic model%%%%%%% f(1) = umax*(N/(Kn+N))*(I/(I+k+((I^2)/kip)))*(B/(KHCO+B))*X; %biomass with-
out glycogen production %f(2) =
umax*(I/(I+k))*((B/(KHCO+B))*(N/(Kn+N))+(Pc/(Kpc+Pc))*(Kn/(Kn+N)))*XT; f(2) =
umax*((I/(I+k+((I^2)/kip)))*(B/(KHCO+B))*(N/(Kn+N))+((Pc/(Kpc+Pc))*(B/(KHCO
+B))*(Kn/(Kn+N))))*XT;
if I>12; f(3)=Rpc*((kli/(I+kli))-((I/(I+kli))+(Kn/(N+Kn))+(KHCO/(B+KHCO))))*Pc; % else f(3)=Rpc*-((Kn/(N+Kn)))*Pc; %f(3)=0; end
if m==1; if N<0.000005 f(4)=0; f(8)=0; f(10)=0; f(11)=0; f(12)=0; N==0.000005;
- 93 -
else if t<=28 f(4) =-Ynx*f(2); else if t<=52 f(8) =-Ynx*f(2); else if t<=76 f(10) =-Ynx*f(2); else if t<=100 f(11) =-Ynx*f(2); else f(12) =-Ynx*f(2); end end end end end else if N<0.000005 f(4)=0; else f(4) =-Ynx*f(2); end end
% end
% f(4) =-Ysx*f(1); %Sulphate comsuption f(9) =-Ypx*f(2); %phosphaspe comsuption (%%%%%intracelluar phosphaete
model) f(5)=Zch*f(1); %chlorophyll generation ti=(((pc/(H))*44)/1000); %from mol/me to g/L tio=(((pc2/(H))*44)/1000); f(6) =kla*(ti-Dis)+klao*(tio-Dis)-1*f(2); %co2 transfer to the medium -
co2cconvert into bicarboante - and co2 desortion to mantain enquilibrium
if B<0.004 %Yco=0; %B==0; f(7)=0;
else
f(7) =-Yco*f(2); %bicarboante consume by the algae + bicarbonate produce in
the reaction CO2 + OH
end return % function [f] = pHmodel(y) global c k1 k2 kw f = zeros(2,1); %%%%% co2 concentration b = y(1); %b=b%h+ cocentration CT = y(2); %c=c%co2 concentration %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% f(1)= ((1+(k1/b)+((k1*k2)/(b^2)))*c)-c*((k1/(b^2))+((2*k1*k2)/(b^3)))*b-CT;
- 94 -
f(2)=
(((k1/(b))+2*(k1*k2/(b^2)))/1+(kw/(b^2))+((k1*c)/(b^2))+((4*k1*k2*c)/(b^3))
)*c-b; return;
- 95 -
12 References
Abd El Baky H, Hanaa El Baz KF, El-Latife SA (2014) Induction of sulfated polysaccharides
in Spirulina platensis as response to nitrogen concentration and its biological evaluation
Journal of Aquaculture Research and Development 5 doi:10.4172/2155-9546.1000206
Baart GE, Martens D (2012) Genome-Scale Metabolic Models: Reconstruction and Analysis.
In: Christodoulides M (ed) Neisseria meningitidis, vol 799. Methods in Molecular
Biology. Humana Press, pp 107-126. doi:10.1007/978-1-61779-346-2_7
Baroukh C, Muñoz-Tamayo R, Bernard O, Steyer J-P (2015) Mathematical modeling of
unicellular microalgae and cyanobacteria metabolism for biofuel production Curr Opin
Biotechnol 33:198-205 doi:http://dx.doi.org/10.1016/j.copbio.2015.03.002
Bertucco A, Beraldi M, Sforza E (2014) Continuous microalgal cultivation in a laboratory-scale
photobioreactor under seasonal day–night irradiation: experiments and simulation
Bioprocess Biosyst Eng 37:1535-1542 doi:10.1007/s00449-014-1125-5
Bezerra RP, Montoya EYO, Sato S, Perego P, de Carvalho JCM, Converti A (2011) Effects of
light intensity and dilution rate on the semicontinuous cultivation of Arthrospira
(Spirulina) platensis. A kinetic Monod-type approach Bioresour Technol 102:3215-
3219 doi:http://dx.doi.org/10.1016/j.biortech.2010.11.009
Borowitzka M (2013) High-value products from microalgae—their development and
commercialisation Journal of Applied Phycology 25:743-756 doi:10.1007/s10811-013-
9983-9
Brown SB, Houghton JD, Vernon DI (1990) New trends in photobiology biosynthesis of
phycobilins. Formation of the chromophore of phytochrome, phycocyanin and
phycoerythrin J Photochem Photobiol, B 5:3-23 doi:10.1016/1011-1344(90)85002-e
Bungay HR (1994) Growth rate expressions for two substrates one of which is inhibitory J
Biotechnol 34:97-100 doi:http://dx.doi.org/10.1016/0168-1656(94)90170-8
Camacho FG, Rodríguez JJG, Mirón AS, Belarbi EH, Chisti Y, Grima EM (2011)
Photobioreactor scale-up for a shear-sensitive dinoflagellate microalga Process
Biochem (Amsterdam, Neth) 46:936-944
doi:http://dx.doi.org/10.1016/j.procbio.2011.01.005
Camacho Rubio F, Acien Fernandez FG, Sanchez Perez JA, Garcia Camacho F, Molina Grima
E (1999) Prediction of dissolved oxygen and carbon dioxide concentration profiles in
tubular photobioreactors for microalgal culture Biotechnol Bioeng 62:71-86
Chaiklahan R, Chirasuwan N, Triratana P, Loha V, Tia S, Bunnag B (2013) Polysaccharide
extraction from Spirulina sp. and its antioxidant capacity Int J Biol Macromol 58:73-78
doi:http://dx.doi.org/10.1016/j.ijbiomac.2013.03.046
Chen CY, Kao PC, Tsai CJ, Lee DJ, Chang JS (2013) Engineering strategies for simultaneous
enhancement of C-phycocyanin production and CO2 fixation with Spirulina platensis
Bioresour Technol 145:307-312 doi:10.1016/j.biortech.2013.01.054
Cogne G, Gros JB, Dussap CG (2003) Identification of a metabolic network structure
representative of arthrospira (spirulina) platensis metabolism Biotechnol Bioeng
84:667-676 doi:10.1002/bit.10808
- 96 -
Converti A, Lodi A, Del Borghi A, Solisio C (2006) Cultivation of Spirulina platensis in a
combined airlift-tubular reactor system Biochemical Engineering Journal 32:13-18
doi:http://dx.doi.org/10.1016/j.bej.2006.08.013
Cornet JF, Dussap CG, Cluzel P, Dubertret G (1992) A structured model for simulation of
cultures of the cyanobacterium Spirulina platensis in photobioreactors: II. Identification
of kinetic parameters under light and mineral limitations Biotechnol Bioeng 40:826-834
doi:10.1002/bit.260400710
Cornet JF, Dussap CG, Gros JB (1998) Kinetics and energetics of photosynthetic micro-
organisms in photobioreactors. In: Bioprocess and Algae Reactor Technology,
Apoptosis, vol 59. Advances in Biochemical Engineering Biotechnology. Springer
Berlin Heidelberg, pp 153-224. doi:10.1007/BFb0102299
Csőgör Z, Kiessling B, Perner I, Fleck P, Posten C (2001) Growth and product formation of
Porphyridium purpureum Journal of Applied Phycology 13:317-324
doi:10.1023/a:1017945513485
De Morais MG, Costa JAV (2007) Biofixation of carbon dioxide by Spirulina sp. and
Scenedesmus obliquus cultivated in a three-stage serial tubular photobioreactor J
Biotechnol 129:439-445 doi:http://dx.doi.org/10.1016/j.jbiotec.2007.01.009
Degen J, Uebele A, Retze A, Schmid-Staiger U, Trösch W (2001) A novel airlift
photobioreactor with baffles for improved light utilization through the flashing light
effect J Biotechnol 92:89-94
Del Rio-Chanona EA, Zhang D, Xie Y, Manirafasha E, Jing K (2015) Dynamic Simulation and
Optimization for Arthrospira platensis Growth and C-Phycocyanin Production
Industrial and Engineering Chemistry Research 54:10606-10614
doi:10.1021/acs.iecr.5b03102
Doshi YK, Pandit AB (2005) Effect of internals and sparger design on mixing behavior in
sectionalized bubble column Chem Eng J (Lausanne) 112:117-129
Dubinsky Z, Stambler N (2009) Photoacclimation processes in phytoplankton: Mechanisms,
consequences, and applications Aquatic Microbial Ecology 56:163-176
doi:10.3354/ame01345
Eilers PHC, Peeters JCH (1988) A model for the relationship between light intensity and the
rate of photosynthesis in phytoplankton Ecological Modelling 42:199-215
doi:http://dx.doi.org/10.1016/0304-3800(88)90057-9
Filali Mouhim R, Cornet JF, Fontane T, Fournet B, Dubertret G (1993) Production, isolation
and preliminary characterization of the exopolysaccharide of the cyanobacterium
Spirulina platensis Biotechnol Lett 15:567-572 doi:10.1007/bf00138541
Fleck-Schneider P, Lehr F, Posten C (2007) Modelling of growth and product formation of
Porphyridium purpureum J Biotechnol 132:134-141
doi:http://dx.doi.org/10.1016/j.jbiotec.2007.05.030
García Camacho F, Gallardo Rodríguez JJ, Sánchez Mirón A, Cerón García MC, Belarbi EH,
Molina Grima E (2007) Determination of shear stress thresholds in toxic dinoflagellates
cultured in shaken flasks: Implications in bioprocess engineering Process Biochem
(Amsterdam, Neth) 42:1506-1515 doi:http://dx.doi.org/10.1016/j.procbio.2007.08.001
Georgiev T, Ratkov A, Tzonkov S (1997) Mathematical modelling of fed-batch fermentation
processes for amino acid production Mathematics and Computers in Simulation 44:271-
285 doi:http://dx.doi.org/10.1016/S0378-4754(97)00059-1
- 97 -
Gilbert SM, Allison GG, Rogers LJ, Smith AJ (1996) Expression of genes involved in
phycocyanin biosynthesis following recovery of Synechococcus PCC 6301 from
nitrogen starvation, and the effect of gabaculine on cpcBa transcript levels FEMS
Microbiol Lett 140:93-98 doi:10.1016/0378-1097(96)00167-x
Goldman JC, Graham SJ (1981) Inorganic carbon limitation and chemical composition of two
freshwater green microalgae Appl Environ Microbiol 41:60-70
Guan X, Qin S, Zhao F, Zhang X, Tang X (2007) Phycobilisomes linker family in
cyanobacterial genomes: Divergence and evolution International Journal of Biological
Sciences 3:434-445
Hasunuma T, Kikuyama F, Matsuda M, Aikawa S, Izumi Y, Kondo A (2013) Dynamic
metabolic profiling of cyanobacterial glycogen biosynthesis under conditions of nitrate
depletion J Exp Bot doi:10.1093/jxb/ert134
Hayashi T, Hayashi K, Maeda M, Kojima I (1996) Calcium Spirulan, an Inhibitor of Enveloped
Virus Replication, from a Blue-Green Alga Spirulina platensis J Nat Prod 59:83-87
doi:10.1021/np960017o
He L, Subramanian VR, Tang YJ (2012) Experimental analysis and model-based optimization
of microalgae growth in photo-bioreactors using flue gas Biomass and Bioenergy
41:131-138 doi:http://dx.doi.org/10.1016/j.biombioe.2012.02.025
Huang S-Y, Chen C-P (1986) Growth kinetics and cultivation of spirulina platensis J Chin Inst
Eng 9:355-364 doi:10.1080/02533839.1986.9676900
Jiménez C, Cossío BR, Niell FX (2003) Relationship between physicochemical variables and
productivity in open ponds for the production of Spirulina: A predictive model of algal
yield Aquaculture 221:331-345 doi:10.1016/s0044-8486(03)00123-6
Joseph A, Aikawa S, Sasaki K, Matsuda F, Hasunuma T, Kondo A (2014) Increased biomass
production and glycogen accumulation in apcE gene deleted Synechocystis sp. PCC
6803 AMB Express 4:17-17 doi:10.1186/s13568-014-0017-z
Kamata K et al. (2014) Spirulina-Templated Metal Microcoils with Controlled Helical
Structures for THz Electromagnetic Responses Scientific Reports 4:4919
doi:10.1038/srep04919
http://www.nature.com/articles/srep04919#supplementary-information
Kantarci N, Borak F, Ulgen KO (2005) Bubble column reactors Process Biochem (Amsterdam,
Neth) 40:2263-2283
Kern DM (1960) The hydration of carbon dioxide J Chem Educ 37:14 doi:10.1021/ed037p14
Keymer P, Lant P, Pratt S (2014) Modelling microalgal activity as a function of inorganic
carbon concentration: accounting for the impact of pH on the bicarbonate system
Journal of Applied Phycology 26:1343-1350 doi:10.1007/s10811-013-0146-9
Klanchui A, Khannapho C, Phodee A, Cheevadhanarak S, Meechai A (2012) iAK692: A
genome-scale metabolic model of Spirulina platensis C1 BMC Systems Biology 6:71
König T (2007) Gewinnung und Charakterisierung antiviraler Wirkstoffe aus aquatischen
Mikroorganismen. Production and characterisation of antiviral compounds of aquatic
microorganisms. Doctoral Thesis, Friedrich-Alexander-Universität Erlangen-Nürnberg
(FAU)
- 98 -
Kumar D, Dhar D, Pabbi S, Kumar N, Walia S (2014) Extraction and purification of C-
phycocyanin from Spirulina platensis (CCC540) Ind J Plant Physiol 19:184-188
doi:10.1007/s40502-014-0094-7
Lau RH, MacKenzie MM, Doolittle WF (1977) Phycocyanin synthesis and degradation in the
blue-green bacterium Anacystis nidulans J Bacteriol 132:771-778
Laurentin A, Edwards CA (2003) A microtiter modification of the anthrone-sulfuric acid
colorimetric assay for glucose-based carbohydrates Anal Biochem 315:143-145
doi:http://dx.doi.org/10.1016/S0003-2697(02)00704-2
Lee E, Jalalizadeh M, Zhang Q (2015) Growth kinetic models for microalgae cultivation: A
review Algal Research 12:497-512 doi:http://dx.doi.org/10.1016/j.algal.2015.10.004
Lee HY, Erickson LE KINETIC AND BIOENERGETIC STUDIES OF SPIRULINA
PLATENSIS IN CHEMOSTAT AND TURBIDOSTAT CULTURES. In:
Biotechnology and Bioengineering Symposium, 1986. pp 463-479
Levert JM, Xia J (2001) Modeling the growth curve for Spirulina (Arthrospira) maxima, a
versatile microalga for producing uniformly labelled compounds with stable isotopes
Journal of Applied Phycology 13:359-367 doi:10.1023/a:1017924422164
Lobatón HF, Suárez CA, Molina A (2011) CFD-Facilitated Flow Field Analysis of Bubble
Columns with Concentric Plates for Biological Applications Chem Eng Technol
34:1490-1496 doi:10.1002/ceat.201000453
Luo HP, Al-Dahhan MH (2004) Analyzing and Modeling of Photobioreactors by Combining
First Principles of Physiology and Hydrodynamics Biotechnol Bioeng 85:382-393
Luo HP, Kemoun A, Al-Dahhan MH, Sevilla JMF, Sánchez JLG, Camacho FG, Grima EM
(2003) Analysis of photobioreactors for culturing high-value microalgae and
cyanobacteria via an advanced diagnostic technique: CARPT Chem Eng Sci 58:2519-
2527
Markou G, Angelidaki I, Nerantzis E, Georgakakis D (2013) Bioethanol production by
carbohydrate-enriched biomass of Arthrospira (Spirulina) platensis Energies 6:3937-
3950 doi:10.3390/en6083937
Menezes JC, Alves SS, Lemos JM, de Azevedo SF (1994) Mathematical modelling of industrial
pilot-plant penicillin-G fed-batch fermentations J Chem Technol Biotechnol 61:123-
138 doi:10.1002/jctb.280610207
Merchuk JC, Wu X (2003) Modeling of photobioreactors: Application to bubble column
simulation Journal of Applied Phycology 15:163-169
Miller AG, Colman B (1980) Evidence for HCO(3)(−) Transport by the Blue-Green Alga
(Cyanobacterium) Coccochloris peniocystis Plant Physiol 65:397-402
Mitsuhashi S, Hosaka K, Tomonaga E, Muramatsu H, Tanishita K (1995) Effects of shear flow
on photosynthesis in a dilute suspension of microalgae Appl Microbiol Biotechnol
42:744-749 doi:10.1007/bf00171956
Molina Grima E, Acién Fernández FG, GarcÃa Camacho F, Camacho Rubio F, Chisti Y
(2000) Scale-up of tubular photobioreactors Journal of Applied Phycology 12:355-368
Nie ZY, Xia JL, Levert JM (2002) Fractionation and characterization of polysaccharides from
cyanobacterium Spirulina (Arthrospira) maxima in nitrogen-limited batch culture
Journal of Central South University of Technology (English Edition) 9:81-86
- 99 -
Nielsen J, Nikolajsen K, Villadsen J (1991) Structured modeling of a microbial system: I. A
theoretical study of lactic acid fermentation Biotechnol Bioeng 38:1-10
doi:10.1002/bit.260380102
Norsker N-H, Barbosa MJ, Vermuë MH, Wijffels RH (2011) Microalgal production — A close
look at the economics Biotechnology Advances 29:24-27
doi:10.1016/j.biotechadv.2010.08.005
Pandit AB, Doshi YK (2005) Mixing time studies in bubble column reactor with and without
internals International Journal of Chemical Reactor Engineering 3
Patel A, Mishra S, Pawar R, Ghosh PK (2005) Purification and characterization of C-
Phycocyanin from cyanobacterial species of marine and freshwater habitat Protein
Expression Purif 40:248-255 doi:http://dx.doi.org/10.1016/j.pep.2004.10.028
Pawlowski A, Fernández I, Guzmán JL, Berenguel M, Acién FG, Normey-Rico JE (2014)
Event-based predictive control of pH in tubular photobioreactors Computers and
Chemical Engineering 65:28-39 doi:10.1016/j.compchemeng.2014.03.001
Pereira S, Zille A, Micheletti E, Moradas-Ferreira P, De Philippis R, Tamagnini P (2009)
Complexity of cyanobacterial exopolysaccharides: composition, structures, inducing
factors and putative genes involved in their biosynthesis and assembly FEMS Microbiol
Rev 33:917-941 doi:10.1111/j.1574-6976.2009.00183.x
Perner-Nochta I, Posten C (2007) Simulations of light intensity variation in photobioreactors J
Biotechnol 131:276-285
Perner I, Posten C, Broneske J (2003) CFD optimization of a plate photobioreactor used for
cultivation of microalgae Chemical Engineering and Technology 26:287-291
Pinsent BRW, Pearson L, Roughton FJW (1956) The kinetics of combination of carbon dioxide
with hydroxide ions Transactions of the Faraday Society 52:1512-1520
Pruvost J, Cornet JF, Legrand J (2008) Hydrodynamics influence on light conversion in
photobioreactors: An energetically consistent analysis Chem Eng Sci 63:3679-3694
Pulz O, Gross W (2004) Valuable products from biotechnology of microalgae Appl Microbiol
Biotechnol 65:635-648 doi:10.1007/s00253-004-1647-x
Pulz O, Sandau P (2009) Untersuchungen zu bioaktiven Wirkungen des Algenpolysaccharids
Calcium-Spirulan aus Arthrospira platensis
Querques N, Cesta M, Santos RM, Chiang YW (2015) Microalgal phycocyanin productivity:
strategies for phyco-valorization J Chem Technol Biotechnol 90:1968-1982
doi:10.1002/jctb.4796
Reichert M (2016) Antiviral Substances from Microalgae Applied in Aquacultures
Anwendung von Antiviralen Substanzen aus Mikroalgen in Aquakulturen.
Ritz M, Thomas JC, Spilar A, Etienne AL (2000) Kinetics of photoacclimation in response to
a shift to high light of the red alga Rhodella violacea adapted to low irradiance Plant
Physiol 123:1415-1425
Rodríguez JJG, Mirón AS, Camacho FG, García MCC, Belarbi EH, Chisti Y, Grima EM (2009)
Causes of shear sensitivity of the toxic dinoflagellate Protoceratium reticulatum
Biotechnol Prog 25:792-800 doi:10.1002/btpr.161
Rubio FC, Camacho FG, Sevilla JMF, Chisti Y, Grima EM (2003) A mechanistic model of
photosynthesis in microalgae Biotechnol Bioeng 81:459-473 doi:10.1002/bit.10492
- 100 -
Sokolichin A, Eigenberger G (1999) Applicability of the standard k-ε turbulence model to the
dynamic simulation of bubble columns: Part I. Detailed numerical simulations Chem
Eng Sci 54:2273-2284
Staats N, Stal LJ, Mur LR (2000) Exopolysaccharide production by the epipelic diatom
Cylindrotheca closterium: Effects of nutrient conditions Journal of Experimental
Marine Biology and Ecology 249:13-27 doi:10.1016/s0022-0981(00)00166-0
Takano H, Arai T, Hirano M, Matsunaga T (1995) Effects of intensity and quality of light on
phycocyanin production by a marine cyanobacterium Synechococcus sp. NKBG
042902 Appl Microbiol Biotechnol 43:1014-1018 doi:10.1007/bf00166918
Trabelsi L, M’sakni N, Ben Ouada H, Bacha H, Roudesli S (2009) Partial characterization of
extracellular polysaccharides produced by cyanobacterium Arthrospira platensis
Biotechnol Bioprocess Eng 14:27-31 doi:10.1007/s12257-008-0102-8
Trujillo FJ, Lee IAL, Hsu CH, Safinski T, Adesina AA (2008) Hydrodynamically-enhanced
light intensity distribution in an externally-irradiated novel aerated photoreactor: CFD
simulation and experimental studies International Journal of Chemical Reactor
Engineering 6
Uusitalo J (1996) Algal carbon uptake and the difference between alkalinity and high pH
("alkalization"), exemplified with a pH drift experiment Scientia Marina 60:129-134
Walter C, Steinau T, Gerbsch N, Buchholz R (2003) Monoseptic cultivation of phototrophic
microorganisms - Development and scale-up of a photobioreactor system with thermal
sterilization Biomol Eng 20:261-271 doi:10.1016/s1389-0344(03)00068-6
Wu LB, Li Z, Song YZ (2010) Hydrodynamic conditions in designed spiral photobioreactors
Bioresour Technol 101:298-303
Wu X, Merchuk JC (2002) Simulation of algae growth in a bench-scale bubble column reactor
Biotechnol Bioeng 80:156-168 doi:10.1002/bit.10350
Xia JL, Nie ZY, Levert JM (2001) Changes in Content, Constituents and Distribution of
Constitutive and Excreted Sugars of Spirulina (Arthrospira) Maxima in Nutrient-
Limited Batch Cultures. In: Chen F, Jiang Y (eds) Algae and their Biotechnological
Potential: Proceedings of the 4th Asia-Pacific Conference on Algal Biotechnology, 3–
6 July 2000 in Hong Kong. Springer Netherlands, Dordrecht, pp 135-146.
doi:10.1007/978-94-015-9835-4_10
Xie Y et al. (2013) Phototrophic cultivation of a thermo-tolerant Desmodesmus sp. for lutein
production: Effects of nitrate concentration, light intensity and fed-batch operation
Bioresour Technol 144:435-444 doi:http://dx.doi.org/10.1016/j.biortech.2013.06.064
Xie Y, Jin Y, Zeng X, Chen J, Lu Y, Jing K (2015) Fed-batch strategy for enhancing cell growth
and C-phycocyanin production of Arthrospira (Spirulina) platensis under phototrophic
cultivation Bioresour Technol 180:281-287
doi:http://dx.doi.org/10.1016/j.biortech.2014.12.073
Zeng X et al. (2012) Autotrophic cultivation of Spirulina platensis for CO2 fixation and
phycocyanin production Chem Eng J (Lausanne) 183:192-197
doi:http://dx.doi.org/10.1016/j.cej.2011.12.062
Zhang Q, Wu X, Xue S, Liang K, Cong W (2012) Study of hydrodynamic characteristics in
tubular photobioreactors Bioprocess Biosyst Eng:1-8
- 101 -
Zlateva P, Denchev D, Simeonov I, Kaimaktchiev A (1993) Mathematical Modelling and
Simulation of Fermentation Process for Citric Acid Production Biotechnology &
Biotechnological Equipment 7:82-84 doi:10.1080/13102818.1993.10818700