Multi-factor kinetic modelling of microalgal biomass

cultivation for optimised lipid production

M. Bekirogullaria,1 , J.K. Pittmanb, C. Theodoropoulosa,*

aSchool of Chemical Engineering and Analytical Science, Biochemical and Bioprocess Engineering Group, University of Manchester, M13 9PL, UKbSchool of Earth and Environmental Sciences, University of Manchester, M13 9PL, UK

Abstract

This paper presents a new quadruple-factor kinetic model of microalgal cultivation considering carbon

and nitrogen concentration, light intensity and temperature, developed in conjunction with laboratory-

scale experiments using the well-studied chlorophyte microalgal species Chlamydomonas reinhardtii.

Multi-parameter quantification was exploited to assess the predictive capabilities of the model. The

validated model was utilized in an optimization study to determine the optimal light intensity and

temperature for achieving maximum lipid productivity while using optimal acetate and nitrogen

concentrations (2.1906 g L-1 acetate and 0.0742 g L-1 nitrogen) computed in a recent publication. It

was found that the optimal lipid productivity increased by 50.9 % compared to the base case, and by

13.6% compared to the previously computed optimal case. Optimization results were successfully

validated experimentally. Such comprehensive modelling approaches can be exploited for robust

design, scale-up and optimization of microalgal oil production, reducing operating costs and bringing

this important technology closer to industrialization.

Keywords

Chlamydomonas reinhardtii, Dynamic kinetic modelling, Microalgal lipids, Cultivation optimization,

Quadruple-factor model.

Nomenclature

1 Currently at: Department of Chemical Engineering, Faculty of Engineering and Architecture, Siirt University, 56100, Turkey

**Corresponding author: k.theodoropoulos@manchester.ac.uk

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TAG Triacylglycerol

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TAP Tris-acetate-phosphate

DCW Dry cell weight

N Nitrogen

S Substrate

I Light intensity

AA Acetic acid

I 0 Local light intensity

L Lipid

X Oil-free biomass

T Incubation temperature K

T 0 Reference temperature K

μ Specific growth rate h-1

μmax Maximum specific growth rate of biomass h-1

K S Substrate saturation constant g S L-1

K i S Substrate inhibition constant g S L-1

μX Specific growth rate of oil-free biomass h-1

μXmax Maximum specific growth rate of oil-free biomass h-1

K XS Acetate saturation constant g S L-1

K i XS Acetate inhibition constant g S L-1

K XN Nitrogen saturation constant g N L-1

K i XN Nitrogen inhibition constant g N L-1

qL Specific growth rate of lipid

qLmax Maximum specific growth rate of lipid g L g X-1 h-1

K LS Acetate saturation constant g S L-1

K i LS Substrate inhibition constant g S L-1

K iNL Nitrogen inhibition constant g N L-1

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Y XS

Yield coefficient for oil-free biomass production with respect to

substrate

g X g S-1

Y XN

Yield coefficient for oil-free biomass production with respect to N g X g N-1

K H pH rate constant L g S-1

Y LS

Yield coefficient for lipid production with respect to substrate g X g S-1

K XI Light saturation constant μEm-2 s-1

K iXI Light inhibition constant μEm-2 s-1

K LI Light saturation constant μEm-2 s-1

K iLI Light inhibition constant μEm-2 s-1

σ Molar extinction coefficient g X-1 L m-1

l The distance between the local position and the external surface of

the system

m

A0X Frequency factors h-1

B0X Frequency factors h-1

Ea X Activation energy of oil-free biomass growth kcal mol-1

Eb X Activation energy of oil-free biomass degradation kcal mol-1

A0L Frequency factors h-1

B0L Frequency factors h-1

Ea L Activation energy of oil production kcal mol-1

Eb L Activation energy of oil degradation kcal mol-1

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1. Introduction

The growing energy demand and concerns about climate change have led to an increased utilization

of renewable resources, particularly biomass, for the sustainable production of fuels and chemicals. In

this regard, microalgae have been proposed as an alternative renewable source for the production of

fuel, chemicals and added-value products due to their outstanding characteristics: mainly producing

high volume of oils and rapid growth rate compare to other terrestrial plants (Gangl et al., 2015, Liu

and Benning, 2013). Microalgal oil consists of glycerolipid triacylglycerol (TAG) that can be converted

into biodiesel, or used for the synthesis of other bioproducts or for other added-value products such

as nutraceuticals. Microalgal metabolic activities are highly versatile and flexible, which makes them

adaptable to different cultivation conditions (Adesanya et al., 2014). This potential of microalgae can

be utilized to control and maximise the production of a targeted compound within microalgae cells.

In both natural and modified systems, the microalgae culture can be exposed to various

environmental factors such as organic carbon and nutrient concentrations, light intensity, pH and

temperature that can simultaneously and antagonistically affect both the biomass production and the

lipid accumulation (Chen and Johns, 1994, Converti et al., 2009). The relationship between carbon

and nitrogen is that the excess carbon fixed from photosynthesis is channelled towards storage

compounds, such as TAG, when available nitrogen concentration is not sufficient for protein synthesis

and cell growth. Independent studies carried out analysing the effect of growth media showed that

adding acetate to the medium led to a enhancing effect in lipid accumulation under N starvation

conditions and created an ‘obese’ phenotype (Goncalves et al., 2015). On the other hand, supplying

unlimited carbon to the medium decreased the secondary responses triggered by changes in

photosynthetic rate. Recent studies carried out by Negi et al. (2016) and Carbone et al. (2018)

showed that under N-depleted conditions the lipid accumulation increased up to about 20 times

compared to N-replete cultures. Apart from the essential carbon availability and macronutrients as

well as micronutrients, favourable environmental conditions (light intensity and temperature) are also

necessary in algae cultivation processes to enhance algal growth, reproduction, lipid accumulation,

algae chemical composition and photosynthetic activity, as well as economic viability of the

processes. The net algae growth rate increases with an increase in light intensity and temperature,

until a certain point where the biomass growth rate is at its maximum. Increasing the light intensity

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and temperature beyond this point does not increase algal growth rate. On the contrary, such an

increase causes photo oxidation, damages the light receptors of algae and reduces the

photosynthetic rate and thus the productivity (Singh et al., 2015, Aleya et al., 2011). An experimental

study undertaken by Yeesang and Cheirsilp (2011) using four different strains, revealed that lipid

content increased in all four strains with increasing light intensity from 33 to 49.5 μE m-2 s-1, but

decreased with light intensity from 49.5 to 82.5 μE m-2 s-1. A similar effect has been recorded for

temperature changes by Yoshimura et al. (2013) showing that increasing temperature from

5,15,20,25,30,35,38 and 45 0C, increases maximum specific growth rate up to a point where the

maximum specific growth rate becomes zero (0.095, 0.207, 0.392, 0.431, 0.496, 0 0 and 0 d-1

respectively). Thus, in order to produce oil-rich microalgal bodies, abiotic stress including nitrogen and

phosphorus deprivation as well as high light intensity and temperature stress can be applied (Zhu et

al., 2014, Singh et al., 2015).

Integrated experimental-computational frameworks that have the ability to predict biomass growth and

lipid accumulation under different growing conditions will help to optimize the process performance,

operating conditions and scale-up of cultivation systems for commercialization and industrial

applicability (Koskimaki et al., 2013, Bekirogullari et al., 2017). Droop, Monod and Andrew models

have been extensively applied to predict biomass growth rate as a function of a single substrate or

nutrient concentration such as phosphorus (Kwon et al., 2013), nitrogen (Eriksen et al., 2006), carbon

(Chen and Johns, 1996) or light (Zhang et al., 1999b). Some researchers have also considered the

simultaneous effect of multiple substrate and environmental factors, such as Solimeno et al. (2015)

who developed a kinetic model based on the Monod model considering inorganic carbon, nitrogen,

temperature and light intensity effects, and Turon et al. (2015) who considered the effect of two

different carbon sources (acetate and butyrate) under heterotrophic conditions. A detailed kinetic

model based on the Monod model has been developed by Al Ketife et al. (2016) considering the co-

limitation of four growth limiting factors N, P, CO2 and light and the model was validated using

experimental data obtained from the growth of Chlorella vulgaris species in externally illuminated

photobioreactor (PBR) over a range of cultivation conditions. However, these aforementioned studies

only simulated biomass growth and considered that lipid accumulation is proportional to it. Adesanya

et al. (2014) developed a mechanistic model based on the Droop model where biomass, starch and

lipid productions have been considered as three different dynamic variables under mixotrophic and

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autotrophic conditions and Figueroa-Torres et al. (2017) produced a multi-parameter kinetic model

based on the Droop compartmentalized approach for the simultaneous optimisation of starch and

lipids production. There are few other models looking into the effects of different growth-limiting

factors such as, temperature and carbon (Goldman and Carpenter, 1974), nitrogen and phosphorus

(Rhee, 1978). Nevertheless, kinetic modelling of simultaneous co-limitation of growth media elements

(nitrogen and acetate) and environmental factors (light and temperature) has not been considered yet.

Additionally, while lipid accumulation has been considered to be proportional to biomass growth, the

effects of abiotic stress towards enhancement of lipid productivity have been recently shown through

a new kinetic model considering biomass growth and lipid accumulation as two different dynamic

variables (Bekirogullari et al., 2017). The model took into account the effect of acetate (as an organic

carbon substrate) and nitrogen (as a replete or limiting nutrient) variation under constant light

illumination on microalgal biomass growth and lipid production, and allowed the optimization of the

process for maximum lipid productivity (Bekirogullari et al., 2017). Nevertheless, it has been observed

that other environmental factors, such as light and temperature, will have a positive or negative effect

on microalgal growth and lipid accumulation (Béchet et al., 2013, Ota et al., 2015, Lee et al., 2015). In

this work, a model that is able to describe both biomass growth and lipid accumulation dynamics

simultaneously as a function of carbon substrate (C), nutrient (N), light (I) and temperature (T) under

photo-heterotrophic growth conditions is presented for the first time.

The model developed by Bekirogullari et al. (2017) was used to establish an optimal strategy for lipid

accumulation in terms of substrate and nitrogen concentration variations under constant light intensity.

Here, this model is expanded in order to develop an improved strategy taking into account light and

temperature variations as well. The developed model, hence, describes in detail biomass growth and

lipid accumulation in the green microalga Chlamydomonas reinhardtii, and includes the simultaneous

effect of four limiting factors, C, N, I and T, under photo-heterotrophic growth conditions. The lipid

accumulation and biomass growth are considered as two different dynamic variables to take

advantage of abiotic stresses towards maximal lipid production. The predictive ability of the developed

photoheterotrophic model for biomass growth rate and lipid accumulation is tested over a range of

growth conditions and environmental conditions. The validated model is then used to compute optimal

initial conditions for maximum lipid accumulation, producing excellent results. The integrated

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experimental-computational framework presented here can be exploited to confidently predict

biomass growth and lipid accumulation, and ultimately to enable robust system design and scale-up.

2. Materials and Methods

2.1. Microorganism and Culture Conditions

Chlamydomonas reinhardtii (CCAP 11/32C), obtained from the Culture Collection of Algae and

Protozoa, UK, was used here as the experimental microalgal strain. The strain was maintained under

photo-heterotrophic conditions in batch cultures as described previously (Bajhaiya et al., 2016). Prior

to bench-scale batch experiments, preculture of the strain was carried out in an environmentally-

controlled incubation room at 25ºC, using 250 mL Erlenmeyer flasks containing 150 mL of Tris-

acetate-phosphate (TAP) medium. The inoculum was then placed on an orbital shaker at 120 rpm for

7-10 days and constant light illumination was provided by a 4ft long 20W high power led T8 tube light,

125µE m−2 s−1light intensity. After achieving the sufficient cell density (7-10 days), experiments were

carried out in experimental culture vessels, Small Anaerobic Reactors (SARs, 500 mL), containing

500 mL of sterile TAP culture medium and 1 mL of algal inoculum. The SARs used in this study were

transparent in order to allow light to travel through the growth culture. The initial concentration of

inoculum, 0.001 g/mL, was identical for all the treatments. Initial concentration was determined

through the measurement of dry cell weight (DCW) by centrifuging 1 mL inoculum culture for 3 min at

3000 g in an Eppendorf Centrifuge 5424. The obtained wet pellet was then washed with cold distilled

water. The washed pellet was centrifuged again for 3 min at 3000 g and weighed on a fine balance

(Sartorius - M-Pact AX224, Germany) to determine the wet biomass. Subsequently, the wet biomass

was dried overnight at 70ºC to determine the DCW.

The initial environmental factor values were 125µE m−2 s−1 and 25ºC for the light intensity and

temperature, respectively. The light intensity and temperature were varied in order to analyse the

effect of light intensity and temperature variations on biomass growth and lipid accumulation. The light

intensity and temperature values that has been tested were chosen according to the experimental

behaviour of system. The experimental procedure started from zero light intensity and 5oC and

increased both light intensity and temperature gradually until reaching the value where the biomass

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growth started decreasing suddenly. Overall, seven light intensities were analysed: 0 µEm−2 s−1,

5µE m−2 s−1, 45 µE m−2 s−1, 105µE m−2 s−1, 125µE m−2 s−1, 135µE m−2 s−1and 155µE m−2 s−1;

and seven temperatures; 5℃, 10℃, 15℃, 20℃, 25℃, 30℃ and 35℃. All culture vessels

were placed into the growth chamber (Fitotron® SGC 120 Plant Growth Chamber) one day before

inoculation to allow the culture vessels to reach the set temperature. Constant light illumination in the

growth chamber was provided by 4ft long standard white fluorescent tubes. When light intensity was

manipulated, the temperature was kept constant at 25℃, and when temperature was manipulated

the light intensity was kept constant at 125µE m−2 s−1. At the start of treatments the pH value was

set at pH=7. The pH of the samples was analysed through the use of a bench type pH meter (Denver

UltraBasic Benchtop Meters, USA). The supernatant and the biomass of the samples were kept

stored at -20ºC for quantification of specific metabolites. All data was statistically analysed by one-

way ANOVA using Tukey post-hoc test performed using Prism v.6.04 (GraphPad).

2.2. Analytical Methods

Biomass concentration, lipid accumulation in dried biomass, acetate and total nitrogen concentration

(linked to NH4Cl concentration), as well as pH of the growth media were measured and quantified

over time during the experiments. The supernatant samples were filtered through 0.45 µm

nitrocellulose membranes (Millipore Ltd.) and then diluted appropriately with HPLC grade water. The

concentration of acetate consumed was quantified using a High Performance/Pressure Liquid

Chromatographer (HPLC) equipped with a Hi- Plex 8 μm 300x7.7 mm column. Here the mobile phase

was sulphuric acid solution (0.05% v/v) and the flow rate of the system was 0.6 mL min-1. The total

nitrogen concentration was quantified by the use of a Total Organic Carbon / Total Nitrogen analyser

(TOC/TN) (TOC-VCSH/TNM-1 Shimadzu). The quantification of lipid concentration was performed by

extracting the lipid from dried biomass using the SOXTEC 1043 automated solvent extraction system.

Hexane was used as organic solvent. After extraction, the hexane was removed by evaporation and

the accumulated lipid was determined gravimetrically. The detailed procedure for the use of HPLC,

TOC-TN and SOXTEC 1043 has been described previously (Bekirogullari et al., 2017).

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2.3. Mathematical Model Construction

2.3.1. Growth kinetics

It has been previously demonstrated (Bekirogullari et al., 2017) that excess carbon supply in the form

of acetate can be inhibitory as seen by dramatically reduced biomass growth and lipid production. It

has also been shown that reduced N supply can enhance lipid accumulation while inhibiting biomass

growth. Therefore, two different kinetic equations were used to describe specific (oil-free) biomass

growth rate (Eq. 1) and lipid production rate (Eq. 2) involving the simultaneous effect of acetate

substrate (denoted as substrate,S , onwards) nitrogen,N , and local light intensity illumination, I (l):

μX=μXmax ∙ S

S+K XS+S2

K iXS

∙ N

N+K XN+ N 2

K iXN

∙ I (l)

I (l )+K XI+I (l)2

K iXI

Eq. 1

μL=qLmax ∙ S

S+K LS+S2

K iLS

∙K iNL

N+K iNL∙

I ( l)

I (l )+K LI+I (l)2

K iLI

Eq. 2

Here μXmaxis the maximum specific growth rate of oil-free biomass (h-1) and qLmax the maximum lipid

specific growth rate (g L g X-1 h-1). K XS ,K XN , K XI , K LS and K LI are the saturation constants (g S L-1)

and K iXS , K iXN , K iXI , K iLS, K iLI the inhibition constants for oil-free biomass growth based on

substrate, nitrogen concentration and light intensity (g S L-1), respectively. K iNL is an inhibition

constant (g N L-1) used here to describe the lipid production dependent on nitrogen concentration.

The local light intensity I (l) is expressed by the Beer-Lambert equation (Béchet et al., 2013, Bernard

et al., 2016):

I ( l )=I 0 .exp(−σXl) Eq. 3

where l is the distance between the local position and the external surface of the system (m), I 0 the

incident light intensity (μEm-2 s-1), σ the molar extinction coefficient and X the oil-free biomass

concentration (Béchet et al., 2013). The final biomass concentration of the acetate-absent treatment

that was performed in (Bekirogullari et al., 2017) was almost zero which points out that the influence

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of CO2 is negligible and therefore it has been discounted in the final biomass growth and lipid

accumulation expressions. The model in Bekirogullari et al. (2017) was a function of substrate and

nitrogen under constant incident light intensity, I 0 as expressed by Eq. 1 and Eq. 2.

In this work, the effect of temperature and of incident light intensity variations on biomass growth and

lipid accumulation has been taken into consideration, hence accounting for environmental changes on

microalgal cultivation processes. Hence, the triple substrate expressions (Eq. 1 and 2) have been

modified into quadruple-factor expressions:

μX=μXmax ∙ f X (S) ∙ f X (N )∙ f X ( I ) ∙ f X (T ) Eq. 4

μL=qLmax ∙ f L(S) ∙ f L(N )∙ f L ( I )∙ f L (T ) Eq. 5

The effect of temperature on (oil-free) biomass growth and lipid accumulation f (T ) is expressed by a

modified version of the Arrhenius equation which accounts for both saturation and inhibition effect of

temperature (Bitaubé Pérez et al., 2008):

f X(T )=A0Xexp [−EaX

R ( 1T − 1T0 )]−B0X exp [−Eb X

R ( 1T − 1T 0 )] (6)

f L(T )=A0Lexp [−EaL

R ( 1T − 1T 0 )]−B0Lexp [−EbL

R ( 1T − 1T 0 )] (7)

The first and the second parts of Eq. 6 and 7 represent the promotion and inhibition effects of

temperature (K), respectively. Ea X ,EaL and Eb X , EbL are the activation energies of growth and

cellular degradation, respectively (kcal mol−1), R is the gas constant (kcal mol−1), T the incubation

temperature (K ), T 0 the reference temperature (K ), and A0X , A0L and B0X ,B0L the corresponding

frequency factors (h−1).

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2.3.2. Rate equations

The kinetic model developed in this work consists of a set of ordinary differential equations (ODEs)

employed for the simultaneous simulation of microalgal biomass growth, lipid production, substrate

and nitrogen consumption and pH change rates.

The microalgal (oil-free biomass) growth rate is described by:

dXdt

=μX . X Eq. 8

The lipid accumulation (lipid production) rate is given by:

dLdt

=μL . X Eq. 9

The substrate consumption rate can be calculated through a mass conservation equation

(Bekirogullari et al., 2017):

dSdt

=−1Y X

S

∙ dXdt

− 1Y L

S

∙ dLdt Eq. 10

where Y XS

is the yield coefficient for oil-free biomass production with respect to substrate and Y LS the

yield coefficient for lipid production with respect to substrate.

The nitrogen consumption rate is given by (Bekirogullari et al., 2017):

dNdt

=−1Y X

N

∙ dXdt Eq. 11

where Y XN

is the yield coefficient for oil-free biomass production with respect to N.

The pH change throughout the cultivation period of the microalgae cultivation system was observed to

be proportional to the substrate consumption rate (Zhang et al., 1999a) and is described by:

dHdt

=−K h ∙ dSdt

Eq. 12

where H is the pH of the medium, and K h is a constant. Consequently, the developed model consists

of 5 ODEs (Eq.8 to 12), with 5 state variables describing the dynamics of biomass growth, lipids

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accumulation, substrate and nitrogen consumption as well as pH change. The model contains 26

parameters (listed in Section 3.1, below), which have been estimated through the procedure

discussed in section 3.3 below.

2.3.3. Parameter Estimation

This work is the first to develop a kinetic model for photoheterotrophic microalgae growth and lipid

accumulation by considering the simultaneous effect of an organic carbon substrate (acetate),

nitrogen, light intensity and temperature, and therefore, the kinetic parameter values for such a

system are not available in the literature. Consequently, a parameter estimation study using the

constructed model (Eq.8 to 12) was carried out in conjunction with in-house derived experimental

data. Data fitting was performed using a non-linear weighted least squares method (Vlysidis et al.,

2011):

Z(kk )=min∑k=1

nk

∑l=1

nl

∑m=1

nm

W k ,l , m (Ck , l ,mpred (kk)−C k ,l ,m

exp )2 Eq. 14

Here kk is the vector of the 26 model parameters, nk is the number of experiments (nk=2), nl is the

number of state variables (nl =5), nm is the number of experimental measurements in time (nm=7), and

Wk,l,m are the weights for each variable used to effectively normalise the computed errors, =

(C k , l ,mpred (kk )−Ck , l ,m

exp ), where C k ,l , mpred are the predicted state variables and C k ,l , m

exp the experimentally

obtained ones. Here the weights were set to Wk,l,m = 1/C k ,l , mexp ,.

The two set of experiments that have been used for the fitting problem are tabulated as Experiment 1

and Experiment 2 in Table 1. The initial concentrations of each experiment were used as the initial

values of the state variables in the ODEs (Eq.8 to 12). The kinetic parameter values were restricted

with an upper and lower bound, which were set according to the experimental behaviour of the system

and values found in the literature. It is worthwhile to note here that parameters used in a previous

paper (Bekirogullari et al., 2017) were allowed to vary by 10% only in order to produce a tighter fit to

experimental results. Reference (Bekirogullari et al., 2017) is given for these parameters as initial

values were taken from this paper and the computed values are very close (most within 1-2%) to the

ones in (Bekirogullari et al., 2017).

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The parameter estimation problem was solved using an in-house developed stochastic optimisation

algorithm (Simulated Annealing) (Vlysidis et al., 2011), coupled with a non-linear programming (NLP)

– based deterministic optimization algorithm. In order to improve the chance of obtaining solutions in

the neighbourhood of the global optimum, the simulated annealing algorithm was used with multiple

restarts. The solution from the simulated annealing algorithm was then used as an initial guess to

compute the final optimum using the MATLAB function fmincon. The optimisation procedure followed

here has been described more in detail previously (Bekirogullari et al., 2017).

Here 10 stochastic optimization runs (restarts) have been used to ensure that the local minima were

avoided. By using the procedure explained above, the values of the 26 parameters as well as their

standard deviations were found and listed in section 3.1. The values of the two constants, T 0 and l

used in the simulations are also given in section 3.1. The resulting time profiles of the 5 state

variables, computed by the kinetic model, and comparisons against experimental datasets including

biomass growth, lipid accumulation, acetate and nitrogen consumption, pH change of the system are

discussed in section 4.2 below. Ultimately, sensitivity analysis was performed by calculating

sensitivities of the parameters via central finite differences for a 10% change in each of the

parameters. The threshold of sensitivity was set to 0.01 hence any sensitivity value above this

threshold was considered “significant”. The results showed that only 1 parameter (K iNL) was

insensitive and it was set to 380.023 as in the literature (Bekirogullari et al., 2017). Sensitivity analysis

have also revealed that the functions used for the light intensity in both oil-free biomass and lipid

production produced the same sensitivities. Therefore, one light intensity function was used for both

oil-free biomass production and lipid production which reduced the model parameters by two (Eq. 15):

f ( I )= I ( l)

I ( l )+K I+I (l)2

K iI

Eq. 15

2.3.4. Process optimization

The validated kinetic model was employed in an optimization study to compute optimal operating light

intensity and temperature using the optimal acetate and nitrogen concentrations (2.1906 g L-1 acetate

and 0.0742 g L-1 nitrogen) computed previously (Bekirogullari et al., 2017) for maximum biomass and

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lipid productivity. The objective was to maximize the lipid, J L, productivity subject to the model

equations (Eq. 8 to 12):

Objective=max (J L¿)¿ Eq. 16

The productivity is defined as:

J L=L−L0t p−t p0

Eq. 17

Here J L is the lipid productivity (m g L−1 s−1), L is the final lipid concentration (m g Lipid L−1)

calculated by Eq.8, L0 is the initial lipid concentration (m g Lipid L−1), t p is the process time (h ).

3. Results and Discussion

A set of experiments were conducted to analyse the effect of varying light intensity and temperature

on biomass growth and lipid accumulation as well as acetate and nitrogen consumption and pH

change. The constructed model was then used to compute kinetic parameter values, which are of

crucial significance for precise system simulations, using the procedure described above. Validation

of the model with the computed kinetic parameters was subsequently performed using sets of

experimental data produced at different operating conditions. The validated model was then used to

compute optimal process operating conditions, for maximum lipid and biomass production.

In order to analyse the impact of the light intensity and temperature on biomass growth and lipid

accumulation and also to guide the model construction and validation process, a series of

experiments were conducted using Small Anaerobic Reactors (SARs, 500ml). Biomass concentration,

lipid accumulation, pH change of the growth media, and acetate and nitrogen concentrations in the

growth media were measured over time for seven different light intensities and seven different

temperature treatments mentioned in section 2.1. As can be seen in Fig. 1, most of the cultures from

different light and temperature treatments reached stationary phase at about 140h, but to make sure

that steady state concentrations were achieved, the cultures were grown up to 192h. The produced

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dynamic profiles were also used to aid the understanding of the effects of modifying light intensity and

temperature on biomass growth and lipid production rates.

The experiments revealed that high light intensities act as system inhibitors, as they can dramatically

reduce biomass growth and lipid accumulation rates (Fig. 1 and 2), which is in agreement with

previous studies (Gordillo et al., 1998, Béchet et al., 2013). In addition, there was no growth observed

for the light-absent (0μEm-2 s-1) media and hence, there was no lipid accumulated (Fig. 2B). For the

two low light intensity treatments (5μEm-2 s-1 and 45μEm-2 s-1), growth rate was slow, while for the

other four treatments under increasingly higher light intensities (105μEm-2 s-1, 125μEm-2 s-1, 135μEm-2

s-1 and 155μEm-2 s-1), cells grew increasingly faster with equivalent growth profiles. The growth

profiles (Fig. 2) revealed that the biomass concentration increased significantly up to a maximum of

0.517 g L-1 as light intensity increased (¿125μEm-2 s-1) (p < 0.0001 for 0 µEm−2 s−1 and

125µE m−2 s−1, one-way ANOVA). Beyond this light intensity value, biomass concentration

decreased. Compared to the 125μEm-2 s-1 light intensity treatment, biomass concentration decreased

significantly (p < 0.0001, one-way ANOVA) both for the light-absent treatment (0μEm-2 s-1) and light-

deficient (5μEm-2 s-1) treatment by approximately 100% and 92%, respectively (Fig. 1A and 2A). For

the other light intensity treatments (45μEm-2 s-1,105 μEm-2 s-1 and 155μEm-2 s-1) biomass decreased

by approximately 38%, 25% and 40%, respectively as can be seen in Fig. 1B and 2B. The light

intensity treatment with 135μEm-2 s-1 did not show any significant difference compared to the 125

μEm-2 s-1 treatment (p < 0.9495, one-way ANOVA). The proportion of lipid production within the cell on

a total dry cell weight basis for all six light intensity treatments was essentially identical (approximately

10-13%), and the difference in volumetric lipid concentration between the light intensity treatments

(Fig. 2) was almost entirely due to the difference in biomass concentration. This finding suggests that

under sufficient acetate (1.05 g L-1) and nitrogen (0.098 g L-1) conditions, light is being assimilated

mainly for cell growth. While increasing light intensity can indeed increase the biomass concentration

and lipid accumulation, as shown here, the inhibition at high light intensities may be either due to

photo-oxidation or to reduction of the photosynthetic rate and thus of productivity. It should be noted

that while all treatments included acetate, the increased light-dependent growth at increasing light

intensities and the inability to grow in the absence of light suggests that the cells do still require light

and therefore the acetate can only limit, but cannot fully replace photosynthesis. The cells are

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therefore growing mixotrophically rather than heterotrophically. The effect of light intensity treatments

on biomass concentration and lipid accumulation is in agreement with previously reported data for C.

reinhardtii where a range of light intensity treatments (0−1200 μEm-2 s-1) were examined (Fouchard

et al., 2009). They found that the biomass concentration increases as the light intensity increases until

a point where photoinhibition starts and biomass concentration decreases. Similar observations were

made for C. reinhardtii by Pottier et al. (2005) and Janssen et al. (2000). The impact of light intensity

variation treatments on biomass growth rate are also in good agreement with other previously

published findings for other microalgae strains, such as Enteromorpha sp. (Sousa et al., 2007),

Botryococcus sp. (Yeesang and Cheirsilp, 2011) and B. braunii (Ruangsomboon, 2012).

C. reinhardtii responded to increases in temperature with increased exponential growth rates until

reaching the optimum temperature for growth (approx. 25oC). Increasing temperature beyond this

point led to sharp declines in biomass growth and lipid accumulation, as can be seen in Fig. 1C, D

and 2C, D. These temperature-dependent profiles are also in agreement with previous studies (Van

Wagenen et al., 2012, James et al., 2011, Ota et al., 2015). For low temperature treatments (5oC and

10oC), biomass and lipid concentration were below detectable levels due to slow growth rate (Fig.

1C). For the moderate temperature treatments (15oC and 35oC), biomass concentration and lipid

accumulation decreased compared to the 25oC treatment by approximately 86% and 83% (for

biomass) (p < 0.0001 for 15℃ and 25℃; p < 0.0011 for 25℃ and 30℃, one-way ANOVA) and

75% and 80% (for lipid) (p < 0.0002 for 15℃ and 25℃; p < 0.0001 for 25℃ and 35℃, one-way

ANOVA), respectively. For the other three temperature treatments (20ºC, 25ºC, and 30ºC) lipid

accumulation growth profiles were essentially the same (Fig. 1C, D) and biomass concentration was

also same for (20ºC, 25ºC) and significantly different compare to (30ºC) (for biomass concentrations:

p = 0.170 for 20ºC and 25ºC; p = 0.1592 for 20ºC and 30ºC; p = 0.110 for 25ºC and30ºC, for lipid

accumulation: p > 0.999 for 20ºC and 25ºC; p = 0.9102 for 20ºC and 30ºC; p = 9524 for 25ºC and

30ºC, one-way ANOVA). Temperature affects the chemical composition of microalgae by impacting

the rate of chemical reactions and the stability of cellular components (Béchet et al., 2013, Lee et al.,

2015). The net algae growth rates increase exponentially as the temperature increases until a certain

point where strains reach their optimum temperature, after which loss of structural integrity leads to

sharp declines in biomass growth rate (Béchet et al., 2013, Lee et al., 2015). Increasing temperature

beyond these points does not increase algal growth rates and causes damage to a wide range of

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proteins, molecules and the light receptors of the algae (Bernard and Rémond, 2012). The impact of

temperature variation treatments are in good agreement with previously published data by James et

al. (2013) for C. reinhardtii where 4 different temperatures were examined: 17ºC, 25ºC, 32 ºC and

35ºC. James et al. (2013) found that biomass growth increases as temperature increases until the

maximum tolerable temperature which was suggested to be between 35ºC -38 ºC. The optimal

growth temperature in nitrogen sufficient media was reported to be 32ºC. The effect of temperature

variation treatments on biomass growth rate are also in good agreement with other previously

reported findings for other microalgae strains, such as C. minutissima (Aleya et al., 2011), C. vulgaris

(Maxwell et al., 1994) and B. braunii (Yoshimura et al., 2013).

3.1. Model validation

The constructed ODE-based kinetic model consists of 5 ordinary differential equations (Eq.8 to 12)

and 26 kinetic parameters. Values of the kinetic parameters were computed by following the

methodology defined in section 3.3. The computed kinetic parameters were as follows;

μXmax=0,275h−1,K XS=0.0624 g S L−1, K i XS=12.40 g S L−1, K XN=0.0812g N L−1,

K i XN=0.6250 g N L−1, K I=45.50μ E m−2 s−1, K iI=297.75 μ E m−2 s−1, A0X=0.6175h−1,

Ea X=25.9243 kcal mol−1, B0X=0.1101h−1, EbX=48.0151 kcalmol−1,

qLmax=0.1512g L g X−1h−1, K LS=4.9155g S L−1,K i LS=0.1375g S L−1, K iNL=380.31g N L−1,

A0L=0.7h−1, EaL=20kcal mol−1, B0L=0.08h−1, Eb L=32kcal mol−1, Y XS=1.1025g X g S−1

,

Y LS=0.048g X g S−1

, Y XN=5.1623 g X g N−1

, K H=0.7606 L g S−1, σ=0.7419 g X−1 Lm−1,

l=0.25m and T 0=293 K . As can be seen in Fig. 3, the resulting model is in excellent agreement

with experimental data for all 4 state variables for experiment 1 and experiment 2 (Table 1). The pH

change profile of the growth culture was also in good agreement with experimental data for

experiment 1 and experiment 2 with small discrepancies. In order to assess the predictive capability

of the developed model, a validation study was carried out by using the conditions (initial acetate and

nitrogen concentrations, temperature and light intensity) of Experiment 3 (also given in Table 1). It

should be noted that all Experiment 3 conditions are different than the ones of Experiments 1 and 2

used for parameter fitting. Fig. 4 depicts the resulting model predictions against the corresponding

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experimental results. As it can be seen, the kinetic model is able to predict the dynamics of the 5

experimentally obtained state variables (biomass growth, lipid accumulation, acetate and N

consumption and pH change) with high accuracy. Apart from the fact that the model shows the right

trend for all 5 state variables, the cumulative errors (sum of square difference between model

predictions, X pred, and data points, X obs , error=∑t=0

t=n

√( Xobs−X pred )2) are also small, not only for the

experiments used for fitting (which should be expected) but also, and more importantly, for the

validation runs. The cumulative error (error=∑t=0

t=n

√(X obs−X pred)2) for each variable is small (the

cumulative error for biomass, X is 0.0619, for lipid, L is 0.0093, for nitrogen is 0.015, for pH, 0.271 and

for carbon substrate, S, it is 0.32). In addition, the corresponding errors for the validated optimization

run are similar. It can therefore be concluded that the detailed interactive (multiplicative) model

constructed here can be utilized for accurate prediction of the dynamic behavior of microalgal batch

experiments. The comparison of the model predictions with other experiments are of the same quality

as for experiment 1 and 2, hence it was not included in the manuscript. Hence, the validated model

can be utilized as an optimization tool to compute optimal operating conditions for maximum biomass

and lipid accumulation for microalgal cultivation systems.

3.2. Optimization of the Process

The operating light intensity and temperature were degrees of freedom in the optimization process.

The upper and lower bounds of the optimization problem were set according to the experimental

behavior of the system. The resulting computed optimal operating conditions for light intensity and

temperature were 130µE m−2 s−1 and 24º C, respectively while acetate and nitrogen concentrations

were 2.19 g L-1 and 0.074 g L-1, respectively. The corresponding optimum lipid productivity was 11.775

mg L-1 d-1, which represents an increase of 50.9 % from the Base Case and an increase of 13.6%

compared to the optimal case computed in (Bekirogullari et al., 2017). Moreover, the computed

optimal biomass productivity was 49.975 mg L-1 d-1. The computed optimal operating conditions were

subsequently validated experimentally. The experimental biomass and lipid productivities were found

to be 51.875 mg L-1 d-1 and 11.662 mg L-1 d-1, respectively. The computed optimal time profiles along

with the corresponding experimental results obtained at the same conditions are depicted in Fig. 5.

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The model predictions are in excellent agreement with the experimental results, which illustrates the

usefulness of the kinetic model for optimal design of experiments.

Coupled kinetic modelling and experimental design of microalgal cultivation is a powerful tool to

understand the interactions between biomass growth, lipid accumulation and environmental growth-

limiting factors. A detailed, experimentally validated kinetic model can be used in optimization studies

to compute optimal growth conditions that yield maximum biomass and lipid productivities. A few

studies have attempted to develop a kinetic model for microalgal biomass growth (Solimeno et al.,

2015, Yoo et al., 2014, He et al., 2012) but not all of them consider the simultaneous and antagonistic

effects of substrate concentration, nitrogen starvation, light intensity and temperature. Additionally,

these studies did not consider lipid production as a different state variable to take advantage of

nutrient stress, which results in higher lipid accumulation. Solimeno et al. (2015) developed a

mechanistic model which considers inorganic carbon limitation, nitrogen availability, temperature and

light intensity effects but the study only simulated biomass growth, considering that lipid accumulation

is proportional to it, which does not allow optimization of biomass and lipid productivities individually.

Consequently, previously developed kinetic models do not allow the accurate prediction of microalgal

cultivation system dynamics under realistic operating conditions. The detailed model developed and

validated in this study is a fully quadruple expression considering co-limitation of acetate (carbon

substrate), nitrogen, light intensity and temperature. It also contains separate expressions for biomass

growth and lipid accumulation, which allows the optimization of individual productivities to be carried

out.

Conclusions

To understand the synergistic interactions between substrate, nutrients and environmental factors, a

comprehensive kinetic model was developed. Kinetic parameters were computed by fitting model

outputs to experimental data for a range of light intensities and temperatures. Model predictions were

validated through comparisons to additional experimental data. An experimentally-validated

optimization study was carried out to identify optimal conditions resulting in maximum biomass and

lipid productivities. The computed optimal lipid productivity increased by 50.9 % compared to the base

case, and by 13.6% compared to a previously-optimized case. This illustrates the effectiveness of

carefully-constructed kinetic models for efficient operation of microalgal systems.

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Supplementary Data

Detailed explanation of light distribution in the reactor based on experimental data as well as

computed sensitivities can be found in the Supplementary information.

Availability of Data and Materials

All data generated or analysed during this study are included in this published article.

E-supplementary data for this work can be found in e-version of this paper online

Competing interests

The authors declare that they have no competing interests.

Acknowledgments

MB would like to acknowledge the financial support of Republic of Turkey Ministry of National

Education.

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List of Figure Captions

Fig. 1. Effect of light intensity (A, B) and temperature (C, D) on dry cell weight (A, C) and total lipid

concentration (B, D) dynamics during photo-heterotrophic growth. Starting temperature for the light

intensity variation treatment experiments was 25ºC and starting light intensity for the temperature

variation treatment experiments was 125μEm-2 s-1. All data are mean ± SE values of 2-3 biological

replicates.

Fig. 2. Effect of light intensity (A, B) and temperature (C, D) on dry cell weight (A, C) and total lipid

concentration (B, D) dynamics during photo-heterotrophic growth. The starting temperature for the

light intensity variation treatment experiments was 25ºC and the starting light intensity for the

temperature variation treatment experiments was 125μEm-2 s-1. All data are mean ± SE values of 2-3

biological replicates. The lower case letters above each bar represent the statistical analysis obtained

from one-way ANOVA. The treatments that do not share same lowercase letters are significantly

different (p < 0.05), as determined by one-way ANOVA. The percentage lipid value as a proportion of

dry weight biomass is indicated above each bar in panels B and D.

Fig. 3. Comparison of model predictions (lines) with experimental data from Experiment 1 (symbols

with error bars) for: (A) biomass and lipid concentration, (B) substrate (acetate) and N consumption.

All data are mean ± SE values of 2-3 biological replicates.

Fig. 4. Comparison of model predictions (lines) with experimental data from Experiment 3 (symbols

with error bars) for: (A) biomass and lipid concentration, (B) substrate (acetate) and N consumption.

All data are mean ± SE values of 2-3 biological replicates.

Fig. 5. Comparison of computed optimal system dynamics (lines) with experimental data (symbols

with error bars) at the same conditions for(A) biomass and lipid concentration, (B) substrate (acetate)

and N consumption, using 2.19 g L-1 acetate and 0.074 g L-1 N, 130 μEm-2 s-1 and 24ºC.

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Table 1: Experiments used for the fitting and validation processes

Experiment Acetate (g L-1) Nitrogen (g L-1) Light (μEm-2 s-1) Temperature (0C)

1 1.05 0.098 125 30

2 1.05 0.098 105 25

3 1.365 0.074 110 28

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Fig.4.

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611

612

Fig.5.

32

613

614

615