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Development of a mathematical model for the calculation

of the CER in a RAMOS device

Nuno Filipe Depetri Araújo

Thesis to obtain the Master’s degree in

Biological Engineering

Supervisors: MSc Andreas Schulte; Prof. Pedro Carlos de Barros Fernandes

Examination Committee:

Chairperson: Prof. Duarte Miguel de França Teixeira dos Prazeres

Supervisor: Prof. Pedro Carlos de Barros Fernandes

Member of the committee: Prof. José António Leonardo dos Santos

December 2014

Acknowledgements

First and foremost, I’d like to thank the wonderful people without whom none of this would have been

possible: my incredibly supporting parents. Thank you for everything.

I’d also like to thank those without whom this would have been a possible, but truly Herculean task: my

sister Daniela, for providing comic relief in the most stressful situations; my wonderful family, for not

asking “how many pages have you written so far?” whenever we’d meet; the best friends a person could

want: André, João, Edgar, Inês, Luísa, Rita, and Sofia; my fellow already-graduated-or-soon-to-be

Biological Engineers; my supervisors Andreas and Pedro for the guidance and support; Emanuel, for the

companionship in our home away from home, and for not letting me forget how to speak Portuguese

while in Aachen; and last but not least, my faithful companion in the long thesis writing nights, my dog

Dot.

Development of a mathematical model for the calculation of the Carbon Dioxide

Evolution Rate in a RAMOS device

Shake flasks are an inexpensive and effective way of reproducibly performing industrially relevant cell

cultivations, and thus are widely used in research. The RAMOS device (Respiratory Activity MOnitoring

System) allows the monitoring of the Oxygen and Carbon Dioxide Transfer Rates (OTR and CTR) of cell

cultures in shake flasks, providing more detailed process knowledge. Another important parameter in

respirometry is the Carbon Dioxide Evolution Rate (CER), the rate at which CO2 is produced and excreted

to the medium by a cell culture. Due to the high solubility of CO2 and the pH-dependent reactions in

which it is involved, a discrepancy between CER and CTR can arise. In this work, a model for the

calculation of the CER in a RAMOS device was developed, with pH and CO2 in the headspace as input

variables. Validation of the model could not be performed; however, the model was able to predict a

reasonable RQ (in comparison with typical values) for the cultivation of E. coli pRSet eYFP-IL6 in TB and

TB-glucose media and E. coli JM109 in LB-glycerol medium, indicating the model’s potential for further

development.

Desenvolvimento de um modelo matemático para o cálculo da taxa de produção de

dióxido de carbono num aparelho RAMOS

Os shake flasks são um meio eficaz e de baixo custo de efectuar culturas celulares de relevância

industrial, sendo por isso muito utilizados em pesquisa. O aparelho RAMOS (Respiratory Activity

MOnitoring System) permite a monitorização online das taxas de transferência de oxigénio e de dióxido

de carbono (OTR e CTR, respectivamente) de culturas celulares em shake flasks, fornecendo informação

de processo mais aprofundada. Outro parâmetro importante em respirometria é a taxa de produção de

dióxido de carbono (CER). Dada a elevada solubilidade do CO2 e as reacções dependentes do pH em que

está envolvido, a CER e a CTR podem apresentar uma diferença significativa. Neste trabalho,

desenvolveu-se um modelo para o cálculo da taxa de produção de CO2 num aparelho RAMOS, tendo a

pressão parcial de CO2 no headspace e o pH do meio como variáveis de input. O modelo não foi

validado; no entanto, o modelo conseguiu prever um quociente respiratório (CER/OTR) razoável para

culturas de E. coli pRSet eYFP-IL6 em meios TB e TB-glucose, e numa cultura de E. coli JM109 em meio

LB-glicerol, indicando o potencial do modelo para futuro desenvolvimento.

Key words: Respirometry, RAMOS, Carbon Dioxide Evolution Rate, Shake flask, Bioprocess monitoring.

1

Index

Table of tables 2

Table of Figures 3

List of abbreviations and symbols 5

1. Introduction 7

1.1. Respiratory activity in fermentation processes 7

1.2. Reactions involving CO2 9

1.3. Solubility of CO2 in fermentation media 10

1.4. Liquid-gas transfer of CO2 11

1.5. Models for calculating the CER 13

1.6. Shaken Bioreactors and the RAMOS device 14

2. CER calculation in the RAMOS device 18

2.1. Non-Dispersive Infrared CO2 sensors 18

2.2. Mathematical model 19

3. Materials and Methods 24

3.1. Characterization of the NDIR sensors 24

3.1.1. Effect of the shaking frequency on the output signal 24

3.1.2. Linearity of pCO2 vs output signal 24

3.1.3. Calibration curves and sensor dynamics 25

3.1.4. Effect of different sensor positions on the output signal 27

3.2. Fermentation examples 27

3.2.1. Growth media 27

3.2.2. Culture conditions 27

3.3. Effect of different gas outlet configurations on the measured

respiratory activity 29

3.4. Automated calculation of CTR and CER 30

4. Results and discussion 32

4.1. Characterization of the NDIR sensors 32

4.1.1. Effect of shaking frequency on the output signal 33

4.1.2. Linearity of output signal vs pCO2 33

4.1.3. Calibration curves and sensor dynamics 33

4.1.4. Effect of different sensor positions on the output signal 35

4.2. Mathematical model: examples simulations and possible validation

methods 37

4.2.1. Examples 37

4.2.2. Effect of the pH on the predicted CER 39

4.2.3. Possible validation methods 42

4.3. Fermentation examples 43

4.3.1. E. coli pRSeT eYFP-IL6 in buffered TB and TB-glucose media 43

4.3.2. E. coli JM109 in LB-glycerol medium 45

4.4. Influence of the gas outlet configuration in the respiratory activity

measurement 46

5. Conclusion and Outlook 49

6. References 50

2

Table of tables

Table 1 - Typical Respiratory Quotient values for various substrates ..................................................... 8

Table 2 - Model equations with respective initial values ...................................................................... 23

Table 3 - Composition of the growth media used in the fermentation assays. The concentrations are

expressed in g.L-1. .................................................................................................................................. 27

Table 4 - Length of the different phases of the measuring cycle .......................................................... 28

Table 5 - Parameters used in the computation of the CER and CTR ..................................................... 30

Table 6 - Calibration curve parameters. ................................................................................................ 34

3

Table of figures

Fig. 1 - Graphical representation of the two film theory. A substance is transported from phase 1 to

phase 2, passing through two stagnant films and an interface. ........................................................... 11

Fig. 2 - The multiple interactions of carbon dioxide within the fermentation broth. ........................... 13

Fig. 3 - a) A specially adapted RAMOS shake flask; b) an in-house built RAMOS device from the

Bioprocesses chair at RWTH Aachen, equiped with six 250mL flasks. .................................................. 15

Fig. 4 - General set-up of a RAMOS device. ........................................................................................... 16

Fig. 5 - OTR profiles for typical metabolic phenomena perceivable with a RAMOS device .................. 17

Fig. 6 - a) Technical drawing of the insides of a sensor (adapted from [39]); b) NDIR CO2 sensor [40].18

Fig. 7 - Schematic representation of an NDIR sensor. ........................................................................... 19

Fig. 8 - Phenomena captured by the model. ......................................................................................... 23

Fig. 9 - Experimental scheme used for assessing the linearity of the IR sensors .................................. 25

Fig. 10 - Experimental set-up for calibrating the sensors and calculating the time constant ............... 25

Fig. 11 - Cutaway drawing of the sensor, evidencing the position of the IR light bulb's filament inside

the sensor housing (adapted from [39]). .............................................................................................. 26

Fig. 12 - Side view of the three different positions tested for their effect in signal noise. ................... 27

Fig. 13 - Schematic illustration of the gas outlet on a RAMOS flask. A - outlet of the flask, filled with a

cotton plug; B - screw cap; C - stainless steel piece; D - o-ring; E – gas tight tubing; F - outlet valve. . 29

Fig. 14 - Flowchart of the automated calculation of CTR and CER ........................................................ 31

Fig. 15 - Effect of different shaking frequencies in the signal of three selected sensors. T=298 K, d0=5

cm, pCO20. ........................................................................................................................................... 32

Fig. 16 - Effect of different shaking frequencies in the signal of three selected sensors, with new filter

definitions. T=298 K, d0=5 cm, pCO20. ................................................................................................ 33

Fig. 17 - Three sensors showing a linear response to increasing carbon dioxide partial pressures.

T=303 K, Flow=33 mL.min-1, d0=5 cm, N=300 rpm. ............................................................................... 33

Fig. 18 - Response of eight sensors to a step increase from 3.8x10-4 to 4.93x10-2 atm of pCO2. T=303K,

flow=10 mL.min-1. .................................................................................................................................. 34

Fig. 19 – Step response of one old sensor and one new sensor, and respective fitting curves.

Step=0.0489 atm, T=298 K, Flow=0.6 L.h-1. ........................................................................................... 35

Fig. 20 – Effect of different shaking frequencies on the signal of two sensors, positioned with the light

bulb filament parallel to the ground. T=303 K, d0=2.5 cm. ................................................................... 35

Fig. 21 – Effect of different shaking frequencies on the signal of two sensors, in an upright position.

T=303 K, d0=2.5 cm. ............................................................................................................................... 36

Fig. 22 – Effect of different shaking frequencies on the signal of two sensors, positioned with the light

bulb filament perpendicular to the ground. T=303 K, d0=2.5 cm.......................................................... 36

Fig. 23 – Hypothetical behavior of the light bulb filament when the sensor is shaken in an upright

position (sensor seen from above). ....................................................................................................... 37

Fig. 24 – pCO2 during a stop-phase in the exponential growth phase, at 2.5 hours in. E. coli BL21

pRSet eYFP-IL6 in TB medium, T=310 K, N=340 rpm, d0=5 cm, VL=0.010 L, Vg=0.271 L, CTR=46 mM.h-1,

CER=53 mM.h-1. ..................................................................................................................................... 38

Fig. 25 - pCO2 during a stop-phase in the end of the stationary phase, at 5.5 hours in. E. coli BL21

pRSet eYFP-IL6 in TB medium, T=310 K, N=340 rpm, d0=5 cm, VL=0.010 L, Vg=0.271 L, CTR=36 mM.h-1,

CER=46 mM.h-1. ..................................................................................................................................... 38

4

Fig. 26 - Dissolved CO2 and bicarbonate during a stop-phase in the exponential growth phase, at 2.5

hours in. E. coli BL21 pRSet eYFP-IL6 in TB medium, T=310 K, N=340 rpm, d0=5 cm, VL=0.010 L,

Vg=0.271 L, pH=7.15, CTR=46 mM.h-1, CER=53 mM.h-1. ........................................................................ 39

Fig. 27 - Dissolved CO2 and bicarbonate during a stop-phase in the end of the stationary phase, at 5.5

hours in. E. coli BL21 pRSet eYFP-IL6 in TB medium, T=310 K, N=340 rpm, d0=5 cm, VL=0.010 L,

Vg=0.271 L, pH=7.65, CTR=36 mM.h-1, CER=46 mM.h-1. ........................................................................ 39

Fig. 28 - pCO2 and dissolved CO2 concentration during a stop-phase at 3 hours into the fermentation.

E. coli BL21 pRSet eYFP-IL6 in TB-glucose medium, T=310 K, N=340 rpm, d0=5 cm, VL=0.010 L,

Vg=0.281 L. ............................................................................................................................................. 40

Fig. 29 - Predicted bicarbonate concentrations for different pH values. E. coli BL21 pRSet eYFP-IL6 in

TB-glucose medium, T=310 K, N=340 rpm, d0=5 cm, VL=0.010 L, Vg=0.281 L. ...................................... 40

Fig. 30 - Predicted CER for different pH values. E. coli BL21 pRSet eYFP-IL6 in TB-glucose medium,

time=3 hours, T=310 K, N=340 rpm, d0=5 cm, VL=0.010 L, Vg=0.281 L. ................................................ 41

Fig. 31 - Bicarbonate concentration during a stop-phase with constant rates of change in pH. Initial

pH is 7.5. ................................................................................................................................................ 41

Fig. 32 - Predicted CER for constant rates of change in pH. E. coli BL21 pRSet eYFP-IL6 in TB-glucose

medium. Initial pH=7.5, time=3 hours, T=310 K, N=340 rpm, d0=5 cm, VL=0.010 L, Vg=0.281 L. ........ 42

Fig. 33 – OTR, CER, CTR-S and CTR-P of a culture of E. coli pRSet eYFP-IL6 in TB-glucose medium.

T=310 K, N=340 rpm, d0=5 cm, VL=0.010 L, Vg=0.270 L. ........................................................................ 43

Fig. 34 - OTR, CER, CTR-S and CTR-P of a culture of E. coli pRSet eYFP-IL6 in TB-glucose medium.

T=310 K, N=340 rpm, d0=5 cm, VL=0.010 L, Vg=0.282 L. ........................................................................ 44

Fig. 35 – RQ (diamonds), TQ-S (squares) and TQ-P (triangles) for E. coli pRSet eYFP-IL6 grown in TB-

glucose (left) and TB (right). .................................................................................................................. 45

Fig. 36 – Measured respiratory activity (OTR, CER, CTR-P, CTR-S) of E. coli JM109 gown on LB-glycerol

media. T=310 K, N=340 rpm, d0=5 cm, VL=0.01 L, Vg=0.270 L. .............................................................. 45

Fig. 37 - RQ ,TQ-S and TQ-P for E. coli JM109 grown in LB-glycerol medium. ..................................... 46

Fig. 38 - OTR of E. coli pRSet eYFP-IL6 grown in TB-glucose. T=310 K, N=340 rpm, d0=5 cm, VL=0.01 L.

Gas outlet configurations: A-normal configuration, B-tubing connected to an open valve, C – tubing

removed, D – tubing and stainless steel piece removed. ..................................................................... 47

Fig. 39 – CTR-P of E. coli pRSet eYFP-IL6 grown in TB-glucose. T=310 K, N=340 rpm, d0=5 cm, VL=0.01

L. Gas outlet configurations: A-normal configuration, B-tubing connected to an open valve, C – tubing

removed, D – tubing and stainless steel piece removed. ..................................................................... 47

Fig. 40 – CTR-P of E. coli pRSet eYFP-IL6 grown in TB-glucose. T=310 K, N=340 rpm, d0=5 cm, VL=0.01

L. Gas outlet configurations: A-normal configuration, B-tubing connected to an open valve, C – tubing

removed, D – tubing and stainless steel piece removed. ..................................................................... 48

5

List of abbreviations and symbols

Abbreviations:

CER - Carbon Dioxide Evolution Rate

CTR - Carbon Dioxide Transfer Rate

CTR-P - Carbon Dioxide Transfer Rate, calculated with the pressure differential

CTR-S - Carbon Dioxide Transfer Rate, calculated with NDIR sensors

IR - Infrared

MFC - Mass Flow Controller

NDIR - Non-Dispersive Infrared

OTR - Oxygen Transfer Rate

OUR - Oxygen Uptake Rate

RAMOS - Respiratory Activity Monitoring System

rpm - Revolutions per minute

RQ - Respiratory Quotient

TQ - Transfer Quotient

TQ-P - Transfer Quotient, calculated with the pressure differential

TQ-S - Transfer Quotient, calculated with NDIR sensors

Symbols:

- Ratio between the interfacial area and the liquid volume

- Gas concentration in the gas side of an interface

- Gas concentration in the liquid side of an interface

- Gas concentration in the liquid

- Concentration of CO2 in the liquid phase film that is in equilibrium with the bulk

concentration in the gas phase

- Concentration of electrolyte

- Gas solubility in pure water

- Gas solubility

- Ion concentration

d - Flask diameter

- Diffusivity

d0 - Shaking diameter

- Volumetric flow of gas into the flask

- Volumetric flow of gas out of the flask

- Henry’s law coefficient

6

- Gas-specific parameter for Schumpe and Weisenberger’s correlation for gas solubility in

salt solutions

- Ion-specific parameter for Schumpe and Weisenberger’s correlation for gas solubility in

salt solutions

- First-order system gain

- First deprotonation constant of carbonic acid

- Global mass transfer coefficient on the liquid side

- Global mass transfer coefficient on the gas side

- Sechenov constant

- Forward reaction rate of the hydration of CO2

- Forward reaction rate of CO2 with HO-

- Reverse reaction rate of the hydration of CO2

- Reverse reaction rate of CO2 with HO-

- Overall reverse reaction rate of CO2 to bicarbonate through the water path

- Pressure in the headspace

- Partial pressure of carbon dioxide

- Partial pressure of a gas

- Partial pressure of oxygen

- Ideal gas constant

- Time

- Stop phase duration

- Temperature

- Headspace volume of the flask

- Volume of liquid in the flask

- Stagnant layer thickness

- Sensor time constant

7

1. Introduction

1.1. Respiratory Activity of Fermentation Processes

In an industrial context, fermentation can be broadly defined as the transformation of matter through

the deliberate cultivation of microorganisms. Mankind has made use of fermentation since ancient times,

producing many different commodities that heavily influenced the shape of today’s society. The Sumerians and

Babylonians were producing a sort of beer before 6000 BC, references to the wine making process can be

found in the Book of Genesis and yeast was used by the ancient Egyptians to make bread [1]. Other important

and well known traditional fermented products include vinegar, yoghurt, silage, cheese and pickled foods, for

example. Nowadays, besides the food and beverage industries, fermentation is employed in a vast array of

applications, such as health-care products (production of antibiotics, vaccines, monoclonal antibodies and

other therapeutic molecules), production of food additives, microbial enzymes (particularly hydrolytic

enzymes), production of industrial platform chemicals and fuel (various alcohols, solvents, polymers for

bioplastics, lipids, organic acids and polysaccharides), wastewater treatment and soil bioremediation, among

others [2].

In a submerged fermentation process, cells are cultured in a liquid medium inside a bioreactor, where

optimal process conditions such as temperature, mixing and pH are maintained. The composition of liquid

media differs from process to process, but in general it consists of a complex aqueous solution of a carbon

source (such as carbohydrates, fatty acids, oils, organic acids), a nitrogen source (corn steep liquor, yeast

extract), minerals and other micronutrients. These substrates are required for the cells to reproduce, form

metabolic products and for general cell maintenance [3]. To obtain energy, the microorganism oxidizes the

carbon source. Anaerobic fermentations take place in the absence of oxygen; in these processes, a myriad of

compounds can act as oxidizing agents, such as sulfate or nitrate. In aerobic processes, oxygen is used as the

electron acceptor, excreting carbon dioxide and water (among other byproducts) as a result.

The measuring of this respiratory activity, or respirometry, is a powerful tool for monitoring and

controlling industrial fermentation processes [4][5]. The most commonly measured variables in respirometry

are the Oxygen Transfer Rate (OTR) and the Carbon Dioxide Transfer Rate (CTR). OTR is the rate at which O2 is

transferred from the gas phase to the liquid phase, and the CTR is the rate of exchange of CO2 between the

liquid and the gas phases. These rates can be readily calculated from in- and outlet gas stream analysis.

The rate at which oxygen is consumed by the microbial culture is called the Oxygen Uptake Rate (OUR)

and, for most cases, its value can be approximated to the OTR due to the limited solubility of O2, such that the

differential term in eq. (1) is negligible [4]:

(1)

Another variable of great interest to fermentation technologists is the Carbon Dioxide Evolution Rate

(CER). This is the rate at which CO2 is produced and released into the liquid medium by the cells. Contrarily to

8

the CTR and the OTR, this rate cannot be measured directly; however, it can be calculated from the

fermentation broth composition if proper mass balances are established with the aid of adequate equipment.

The ratio of the net molar quantity of CO2 evolved by a microorganism (CER) and the molar quantity of oxygen

accordingly consumed (OUR) is called the Respiratory Quotient (RQ). The RQ provides precious information

about the state of a culture, such as the substrate on which the microbe is growing. Substrates that are highly

reduced, such as alkanes, will naturally require more oxygen per carbon atom to be completely oxidized than

highly oxidized substrates. Table 1 shows the typical respiratory quotients for several different substrates [6].

Table 1 - Typical Respiratory Quotient values for various substrates [6]

Substrate RQ

Glucose 1.00

Methanol 0.67

Ethanol 0.67

Acetate 0.80

Propionate 0.75

Lactate 1.00

Glycerol 0.75

Citrate 1.33

Formate 0.50

Oxalate 4.00

Examples of the use of RQ include investigations of microbial processes in soil and litter [7], l-lysine

production [8], oxygen supply of microaerobic fermentations for 2,3-butanediol production [9], controlling

baker’s yeast production [10], and monitoring of biological wastewater treatment [5].

While the OUR can usually be approximated to the OTR, the same cannot be assumed for the CTR and

the CER. Carbon dioxide is highly soluble, and although its solubility does not depend on the pH [11], its

reaction with water to form carbonic acid and its subsequent dissociation into bicarbonate and hydrogen ions

further contributes to the accumulation of carbon dioxide and bicarbonate. At pH>6.5, the amount of total

dissolved CO2 (in both carbon dioxide and bicarbonate forms) in fermentation broths can be one to two orders

of magnitude greater than that of O2 . The rate of change in this concentration can be such that a significant

difference between CER and CTR values arises [4]. For example, at pH 6.3, half of the total dissolved carbon

dioxide is in the form of bicarbonate. An increase of 0.2 pH units makes more than 10% of the dissolved CO2

convert to bicarbonate. Changes in pH (such as those caused by pH control) can have a great effect on the

amount of CO2 transferred to the gas phase, which can lead to misunderstanding metabolic activity if the effect

of pH shifts is not taken into account [5].

9

1.2 Reactions involving carbon dioxide

Since the cell membrane is relatively impermeable to ionic species, CO2 resultant from respiratory

activity enters the broth in the dissolved state [12]. Carbon dioxide can either be transferred to the gas phase

or be hydrated to carbonic acid according to the reaction given by eq. (2)

(2)

If this reaction is uncatalyzed and the pH is lower than 8, it is freely reversible and the forward

reaction occurs at a very slow rate [11]. Carbonic acid quickly dissociates to bicarbonate and hydrogen ions.

(3)

Combining equations (2) and (3) yields the overall reaction, given by eq. (4).

(4)

The reaction described by eq.(2) is a second order reaction. However, it can be treated as a pseudo-

first order reaction if the concentration of water is assumed to be constant and equal to 55.6 M [13]. The

overall equilibrium constant is then given by eq.(5).

(5)

Bicarbonate may undergo a deprotonation to yield carbonate and hydrogen ions (eq. (6)).

(6)

This reaction is extremely slow [11] and can be considered negligible for the usual pH range at which

fermentations take place (pH 4-8) [4]. At high pH values, CO2 can also react with hydroxide ions to yield

bicarbonate ions [5][13][14].

(7)

This mechanism competes with the water path (eq. (4)) to form bicarbonate, being dominant at

pH>8.5 [13]. The following equilibrium relations for pure water (eqs. (8-10)) give an idea of the relative

abundance of the chemical species involved in the reactions described above [15]:

(8)

(9)

(10)

10

Carbon dioxide may also interact with proteins present in the fermentation broth. For example,

formation of carbamates can take place through the interaction between dissolved CO2 and free proteic amino

groups. This reaction is favoured at pH values above the isoelectric point of proteins and competes directly

with the hydration of CO2 [11]. Also, carbonic acid binds strongly with positively charged groups from proteins.

This interaction can affect the hydration equilibrium by diminishing the carbonic acid concentration, but

eventually the process achieves an equilibrium state [11].

Carbon dioxide reacts with many other components of the media, which can affect the equilibria

involved in the reactions listed above, as well as changing the broth’s composition. Although a more detailed

understanding of all of the reactions involving CO2 in culture media is desirable, more research needs to be

done to know how negligible these minor reactions are [11].

1.3 Solubility of CO2 in fermentation media

The solubility of a gas in equilibrium with a liquid can be calculated by the Henry’s law, depending on

the temperature and pressure of the gas/liquid system [11].

(11)

Cg is the gas solubility, Pg is the gas partial pressure and h(T) is the temperature-dependent Henry’s law

coefficient for that gas. Henry’s law is applicable as long as the concentration of dissolved gas is small and the

temperature and pressure are far from the critical values [11]. Several correlations for the CO2/water system’s

Henry’s coefficient can be found in the work of Sander[16].

Fermentation broths are chemically complex systems, containing substances that might increase or

decrease the solubility of gases. Electrolytes reduce the solubility of gases, in what is known as a “salting-out”

effect [11][17]. The effect of the concentration of a single electrolyte on a gas’s solubility has been described by

Sechenov (eq. (12)) [11][17].

(12)

Cg,0 is the gas solubility in pure water, KS is the Sechenov constant (dependent on the pressure,

temperature, gas and electrolyte) and Cel is the electrolyte’s concentration. This empirical relation holds well

for moderate salt concentrations; after a certain critical concentration value, the calculated solubilities are too

low. A correlation for multiple electrolyte solutions (eq. (13)) was developed by Schumpe and Weisenberger

[17]:

(13)

11

In eq.(13), hi and hg are temperature dependent parameters specific for each ion and gas, respectively.

Ci is the concentration of each ion. Values of hg and hi can be found in the work of Schumpe and Weisenberger

[17].

Besides ions and salts, many organic solutes can be present in fermentation media, such as sugars,

alcohols or fatty acids. The effect of sugars concentration on gas solubility can also be calculated with eq.(13).

Some compounds such as small chain alcohols may even enhance the dissolution of CO2. The presence of living

cells that constantly alter the fermentation broth composition further adds to the complexity of these systems,

making it very difficult to accurately predict the solubility of CO2. [11]

1.4 Liquid-gas transfer of CO2

Carbon dioxide is a respiratory byproduct of aerobic processes. Its accumulation in culture media can

have inhibitory effects on microbial growth, enzyme activity and in extreme cases lead to cell lysis [11]. Proper

removal of CO2 from media is thus of paramount importance for fermentation processes.

The two film theory of gas absorption is a useful model to describe mass transfer between two

different phases. This theory states that when two phases are in contact, an interface is formed; a substance

that is being transported from one phase (having a bulk concentration C1, in mol.m-3

) to the other phase (with a

smaller concentration C2) has to be transported from the first phase through the interface, and from the

interface to the second phase (fig. 1).

Fig. 1 - Graphical representation of the two film theory. A substance is transported from phase 1 to phase 2, passing through two stagnant films and an interface.

The theory assumes that both phases are perfectly mixed, thus having a homogeneous concentration

of the present substances; a stagnant film of fluid is formed on each side of the interface; it is assumed then

that there is no transfer resistance in the bulk of the fluids and in the interface, and that all of the resistance is

in the transport through the films. The driving force for mass transfer results from the concentration gradients

near the interface, and the main transport mechanism is diffusion [18]. In the particular case of CO2, phase 1 is

the liquid phase and phase 2 is the gas phase. The mass transfer flow rate (mol.s-1

.m-2

) can be expressed by eq.

(14).

1 2

12

(14)

kL and kG (m.s-1

) are the liquid and gas film coefficients, and are equivalent to the ratio between the

substance’s diffusivity and the thickness of the stagnant film

. The thickness of the film depends on

several factors such as agitation, temperature, and the physical properties of the fluid [11]. The volumetric

molar flow, Q (mol.m-3

.s-1

), is given by equation (15), with a being the ratio between the interfacial area and

the liquid volume.

(15)

The interfacial concentrations are related by the Henry’s law coefficient for CO2, hCO2

, dependent on

the temperature and liquid (eq. (16)) [18].

(16)

Since the interfacial concentrations are not usually known, a global mass transfer coefficient and a

global driving force are employed (eq. (17))

(17)

The product KLa is the volumetric mass transfer coefficient and CL* is the concentration of CO2 in the

liquid side of the interface that is in equilibrium with the bulk concentration in the gas phase

.

Combining equations (15) to (17) yields the relationship between the mass transfer quotients given by

equation (18) for the liquid side.

(18)

For poorly soluble gases, such as O2 and CO2, the Henry’s law coefficient is high and kG >> kL. Therefore,

KL kL, meaning that the main resistance to mass transfer lies on the liquid side [11][12][18]. In the liquid film,

if the hydration reaction is fast enough, it is plausible to assume that the transfer of CO2 is influenced by the

production or consumption of bicarbonate [5]. However, as demonstrated by Royce et al [12], this effect is

negligible compared to the CTR for usual conditions of microbial cultures. Thus, the exchange of CO2 is

assumed to be a purely physical process.

Other models for gas absorption/desorption in/from agitated liquids have been developed by a

number of researchers, and can be divided mainly in three types of model (with the two film theory being one

of them). The still surface approach states that both diffusive and convective mass transfer coexist, with the

convective mechanism being more important with the distance from the interface, until it becomes the

dominant mechanism. This model avoids the abrupt break between convective and diffusive mechanisms

proposed by the stagnant film approach; a downside of this model is that the transfer coefficient that can be

obtained from this model includes two hydrodynamic parameters, instead of only one in the case of the

13

stagnant film model [11]. This model is described in depth in the work of Danckwerts [19]. The third type of

model is based on the surface-renewal approach. In these models, the transport of a substance between two

phases relies on the substitution of patches of liquid at the interface with elements from the bulk of the liquid.

While these patches are at the gas-liquid interface, the gas may diffuse into or out of the liquid [20]. This

motion may be created by agitation of the liquid. The mass transfer coefficient derived with this approach is

proportional to the square root of the product between the diffusivity and a system-specific hydrodynamic

parameter. A more thorough description of models of this type can be found in the work of Perlmutter [21].

1.5. Models for calculating the CER

Figure 2 shows a simplified scheme of the plethora of paths that the evolved CO2 can take.

Fig. 2 - The multiple interactions of carbon dioxide within the fermentation broth.

This complex net of reactions in which CO2 can partake makes CER a difficult parameter to quantify.

Some models for obtaining its value can be found in the literature. In the work of Royce [4], a model was

developed that could predict the discrepancy between CER and CTR during fed-batch fermentations of

Escherichia coli. Instead of explicitly validating the model (requiring quick liquid sample analysis or a carbon

balance), a fermentation system that produces a simple and reproducible growth curve is employed. A phase of

constant glucose feeding, during which the TQ (transfer quotient, CTR/OTR) is equal to the RQ, creates a

steady-state CO2 transfer situation. Since the RQ remains fairly constant during this phase, the model can be

validated by causing known perturbations in the medium pH and feeding rate in order to cause changes to the

CTR. Spérandio and Paul [5] constructed another model for predicting the CER in biodegradation experiments,

and a similar validation strategy was used. Neeleman et al [22] designed a Kalman filter to be used as a

software sensor in order to predict the CER in bicarbonate buffered media. A solution of known concentration

of bicarbonate was continuously fed to a reactor containing medium without cells, in order to simulate the

CER. Measurements of the pH and the total bicarbonate (dissolved CO2 and bicarbonate) in the reactor as well

as off-gas analysis were used to calculate the CER and adjust the Kalman filter’s parameters. It was then

14

successfully applied to an insect cell cultivation in a bench top fermenter, being able to correctly predict the

total bicarbonate and thus the CER. In the work of de Jonge et al [14], a model allowing the reconstruction of

the CER and OUR in highly dynamic conditions was created. The model was used successfully to reconstruct the

OUR and CER of a continuous Penicillium chrysogenum culture to which a glucose pulse was applied. Other

examples in the literature are the works of Kóvacs et al [23] for aerobic thermophilic sludge digestion, Goudar

et al [24] for the estimation of OUR and CER in high density mammalian cell perfusion cultures, Wu et al [25]

for the estimation of the RQ in the continuous culture of Saccharomyces cerevisiae.

1.6. Shaken Bioreactors and the RAMOS device

The initial phases of process development usually comprehend the screening and optimization of

producing strains, cultivation media and conditions; with so many different variables to test, the number of

experiments that have to be performed will naturally be very high. To minimize costs and maximize the amount

of obtainable information, shaken bioreactors with small volumes are vastly employed. These are the most

widely used fermentation/cell culture systems in academic and industrial research [26], ranging in volume from

microtiter plates to a few hundred milliliter shake flasks. Büchs estimates that 90% of all cell culture

experiments make use of shake flasks at some point [26], and for good reason: it is an inexpensive and

effective way of reproducibly performing many types of industrially relevant cell cultivations [27]. Besides their

usefulness in the development and scale-up of processes, tasks such as drug discovery, elucidation of metabolic

pathways, strain development and optimization can be carried out [26][28]. Büchs [26] states that shaken

bioreactors are underestimated by biochemical engineers; since these systems are extremely simple, there is

no significant amount of dedicated fundamental research. Shaken systems are usually employed in the first

stages of process development, and if wrong decisions regarding strains, media and/or culture conditions are

made, it can be very costly or even impossible to revert the negative results on more advanced stages of

process development. Even if no problems are encountered later on, and since the growth conditions during

the screening phase can be very different from the conditions in the production phase, insufficient knowledge

about important scale-up parameters (such as OTR or power input for shear-sensitive cells) can also hide the

potential of better strain and/or media candidates [26][29].

The limited volume/size of these fermentation systems can affect negatively the amount and quality

of information that can be obtained. As Suresh et al [28] point out, in the case of OTR measurement for

example, some methods require the measurement of the dissolved O2, usually done with submerged

electrodes. In this case, the size of the electrodes is not negligible in comparison to the size of the vessel, and

can affect the inherent hydrodynamics of the process. However, non-invasive optical sensors have been used

for monitoring of dissolved oxygen [30], dissolved CO2 [31] and pH level [32], having the advantage of not

interfering with the fermentation course. Another well known shaken system is the BioLector®, produced by

m2p-labs, allowing the monitoring of dissolved oxygen, biomass concentration, concentration of fluorescent

compounds and pH in 48-well microtiter plates [33].

15

The RAMOS device (Respiratory Activity Monitoring System) was created by Anderlei et al [34][35] and

developed at the chair of Bioprocessing from RWTH Aachen, and allows the online measurement of the OTR

and the CTR of cell and microbial cultures in modified shake flasks, bringing together the simplicity and

widespread use of these vessels with deeper knowledge on cultivation conditions and phenomena. This device

has been used for several applications, such as determining oxygen limitation in shake flasks, screening of

microorganisms, optimizing media, investigating secondary substrate limitations, process development and

optimization, and monitoring of pre-cultures for fermentations in stirred reactors [36].

In this system, up to eight modified Erlenmeyer flasks can be used. Each of these flasks is adapted with

a gas inlet, a gas outlet, a feed inlet, and a modified top for lodging an electrochemical O2 sensor (fig. 3a).

These vessels are secured onto a base that is then latched onto an orbital shaker (fig. 3b). Commercial versions

are produced by HiTec-Zang GmbH. The apparatus pictured in figure 3b is the typical in-house built RAMOS

device used at the chair of Biochemical Engineering from RWTH Aachen.

Fig. 3 - a) A specially adapted RAMOS shake flask; b) an in-house built RAMOS device from the Bioprocesses chair at RWTH Aachen, equiped with six 250mL flasks.

The fed gas flow is set by a mass flow controller (MFC); it is then distributed by the flasks via an eight-

way splitter. After the splitter, the gas flows to each flask through capillaries; all eight capillaries have the same

length to ensure equal pressure losses and thus avoiding preferential flow. The flow of gas into or out of the

flask is enabled or disabled by two valves, one placed upstream from the gas inlet and the other one placed

downstream from the gas outlet. The gas in- and outlet are equipped with sterile cotton plugs. After the inlet

valve there is also a differential pressure sensor. The O2 sensor is separated from the gaseous phase by a sterile

membrane. O-rings in all of the flask ports ensure that these are gas tight. The data from the sensors is

continuously fed to a processing unit, and the OTR and CTR calculations are performed with a specific software.

A simplified scheme depicting the general set-up of the device is presented in fig. 4.

16

Fig. 4 - General set-up of a RAMOS device.

Throughout a RAMOS measurement, a cycle consisting of three phases with different lengths is

repeated. In the first phase (rinse phase), both valves are open and air is flushed into the flask, with such a flow

that gas concentrations and hydrodynamics inside the flask closely resemble those of a normal Erlenmeyer

flask with a sterile barrier (cotton plug, for example). In this way, results obtained with the device can be

transferred to normal shake flasks [35]. Before the start of the next phase, the O2 sensors are automatically

calibrated using the known steady-state gas composition to compensate for signal drift.

In the second phase (stop phase), the valves are closed, and the respiratory activity of the cell culture

causes the O2 partial pressure to decline, thus inducing the signal of the O2 sensor to decay. The OTR is

calculated with equation (19). Here, Vg is the headspace volume, VL is the liquid volume, R is the gas constant, T

is the temperature and pO2 is the oxygen partial pressure in the headspace.

(19)

Since the pressure differential in the flask headspace is generated by the difference between the

exchanged oxygen and carbon dioxide, the CTR value is obtained with the calculated OTR value and the

pressure variation during the stop phase, according to equation (20):

17

(20)

Finally, in the third phase (high flow phase), the valves are opened and the flasks are flushed with a

higher flow rate than in the rinse phase. Gaseous compounds accumulated during the previous phase are

removed and normal shake flask conditions are quickly reestablished.

In figure 5 are some examples of typical metabolic phenomena that can be perceived with a RAMOS

device (adapted from [34]):

Fig. 5 - OTR profiles for typical metabolic phenomena perceivable with a RAMOS device

18

2. CER calculation in the RAMOS device

In the present work, a novel method for the calculation of the CER in a RAMOS device is presented,

based on the CTR measuring method developed by Hansen, which uses Non-Dispersive Infra Red (NDIR) CO2

sensors [37]. An estimate for the CER in each stop-phase is obtained with a mathematical model, taking as

inputs the evolution of CO2 in the headspace during this phase and the corresponding pH value, which is

measured offline by sampling normal shake flasks running in parallel. Online measurement of pH in a RAMOS

device has been done with direct measurement with an H+ electrode in a specially adapted flask [38], and also

with pH sensitive sensor spots [32]. In the work developed by Scheidle et al [32], offline pH measurements

were made in parallel normal shake flasks to test the accuracy of the online measurements made with the

sensor spots, presenting a maximum difference of 0.05 pH units, showing that good estimates for the pH

profile in a RAMOS flask can be obtained from offline measurements.

2.1. Non-Dispersive Infrared CO2 sensors

The calculation of the CTR via the pressure differential generated during the stop phase is state-of-the-

art, but there are some inconveniences pertaining to this method. The flask needs to be gas tight in order for

the measured differential pressure to be relevant for the calculation, driving up the vessel’s cost. Since it’s an

indirect method that relies on pressure differential, it can be insensitive, since pressure changes are usually

very small, and temperature changes inside the flask are not picked up by the external temperature sensor. It is

also insensitive to pressure changes due to the accumulation of volatile metabolic byproducts, for example.

In this work, a direct method, developed by Hansen [37], for measuring the transfer of CO2 in the stop

phase is employed, making use of NDIR CO2 sensors, attached to the feed port of the flask, to directly measure

the amount of CO2 (fig. 6). These are incorporated with temperature compensation and are linearized by the

manufacturer, meaning that the output signal is linearly proportional to the volumetric percentage of CO2. The

output signal range is 0.4-2 V, corresponding to 0-5% volume of CO2 at atmospheric pressure.

Fig. 6 - a) Technical drawing of the insides of a sensor (adapted from [39]); b) NDIR CO2 sensor [40].

The working principle of these sensors is based on the absorption of IR light by CO2 and the

pyroelectric characteristics of some materials. Contrary to thermoelectrics (thermocouples), which generate a

16.6 mm

20 mm

19

steady voltage when two different metal junctions are held at two different but constant temperatures,

pyroelectrics generate charge in response to a change in temperature [41]. A schematic representation of the

general working principle of this type of sensors is shown in figure 7.

Fig. 7 - Schematic representation of an NDIR sensor.

Inside the sensor housing, an incandescent light bulb produces a pulse of infrared light, within a range

of wavelengths (3-5 μm). The light travels through an optical path, and a fraction of light of a specific

wavelength is absorbed by the CO2 molecules in the gas sample. Before reaching the pyroelectrical IR detector,

the remaining light is filtered such that only light with the desired wavelength is detected. The radiation raises

the sensor’s temperature and produces a momentaneous charge. When the detector is no longer irradiated, its

temperature diminishes and an opposite charge is generated. These small electric charges are amplified and

converted to a voltage signal inside the sensor housing [40]. A reference signal is created by having another

sensor that is equipped with a different optical filter that allows a different wavelength of light to pass. Light of

this wavelength is not absorbed by the gas molecules. The signal is compared to the reference signal and, after

processing and temperature compensation, an output signal is produced.

2.2. Mathematical model

The first step of the model is to describe the evolution of pCO2 in the headspace during the stop-

phase. The general equation for the CTR during a RAMOS measurement, regardless of the phase, is as follows:

(21)

Fout and Fin are the volumetric flow rates of exit and inlet gases, pCO2 and pCO2,in are the CO2 partial

pressures inside the flask and in the inlet air stream, respectively, Vg is the headspace volume, VL is the liquid

volume, R is the gas constant and T is the temperature.

As described in section 1.6, the gas in- and outlet are closed during the stop-phase. The gas flow rates

are then equal to zero and equation (21) is reduced to equation (22):

(22)

A second degree polynomial is used to model the time profile of pCO2 during the stop-phase (eq. (23)).

20

(23)

The differential term in eq. (22) then becomes

(24)

As demonstrated by Hansen [37] the term a is given by equation (25):

(25)

where pCO2,rinse is the CO2 partial pressure during the rinse phase. Thusly, eq. (23) becomes

(26)

For simplicity, it will be assumed that the flow of gas out of the flask is equal to the incoming flow.

As shown by Hansen [37], the IR sensor can be treated as a first order system. For this type of systems,

the response to a sudden increase in its input is not immediate [42]. For a system with a gain K and a time

constant , the response to a step increase M in its input is given by equation (27):

(27)

The time constant is the time it takes for the system to reach 63.2% of the response to a step increase

in its input (1-e-10.632). Hansen [37] found the sensors to have a large time constant (ca. 0.03 hours), and

thusly, to take this dynamic effect into account, a differential equation system has to be solved:

(28)

(29)

In this model, the parameter

is calculated from the last 10% rinse-phase points. The

evolution of CO2 in the headspace during this time period is modeled as a first-degree polynomial; to take into

account the time constant, the sensor signal relative to this interval is fitted with eq. (29), using the first-degree

polynomial coefficients as fitting parameters. The first-order term of this polynomial corresponds to

.

The second step of the model is calculating the evolution of the dissolved carbon dioxide, as well as

that of bicarbonate. Knowing these variables, the calculation of the CER is done with equation (30).

(30)

21

Here, the index 0 refers to the initial value and tsp refers to the length of the stop-phase.

The time profile of the CTR can be calculated by solving eq. 31, with

as the initial value.

(31)

Another way to express the CTR is through eq. (32):

(32)

with KLaCO2

being the volumetric mass transfer coefficient and hCO2

the Henry’s law coefficient for CO2.

Deriving eq. (32) and combining the result with eq. (31) yields a differential equation for the dissolved CO2 (eq.

(33)), with an initial value of

.

(33)

The Henry’s law coefficient for CO2 in pure water (in mM.atm-1

) is calculated with the correlation given

by Zheng et al [43].

(34)

The ratio of mass transfer coefficients for O2 and CO2 is proportional to the ratio of their diffusivities

[12].

(35)

Even though the diffusivities are dependent on the medium composition, their ratio is not [12]. The

volumetric mass transfer coefficient for O2 is calculated with the correlation given by Maier in the work of

Mehmood et al [44] for low viscosity media in shake flasks (eq. (36)).

(36)

N is the shaking frequency (min-1

), VL is the liquid volume (mL), d0 is the shaking diameter (cm) and d is

the flask’s largest diameter (cm). With the diffusivities ratio and the mass transfer coefficient for O2 it is now

possible to obtain the value of KLaCO2

.

As discussed in sections 1.3 and 1.4, the ionic strength of the medium as well as the presence of

several different chemical species affect both the diffusion and the solubility of CO2, which in turn affects the

values of the Henry’s coefficient and the volumetric mass transfer coefficient. For simplicity’s sake, these are

assumed to be the same as for pure water and constant throughout the fermentation. Also, the high ionic

22

strength of some fermentation broths may affect the rates and equilibria of the reactions involving CO2, but for

most cases concentrations can be used instead of activities [4].

In the calculation of the bicarbonate concentration, dissociation of bicarbonate to carbonate and the

interactions of CO2 and carbonic acid with proteins were ignored. According to Royce [4], the effect of these

reactions can be neglected for the usual pH range at which fermentations take place (pH 4-8). As stated in

section 1.2, bicarbonate may be formed through two paths: hydration of CO2 to carbonic acid and subsequent

deprotonation (eq. (37)), or through the reaction of CO2 with hydroxide ions (eq. (38)).

(37)

(38)

The mass balance to bicarbonate is expressed by equation (39):

(39)

The deprotonation of carbonic acid is a very fast reaction [4] and is considered to be in equilibrium.

Thus, the concentration of carbonic acid can be expressed in terms of bicarbonate concentration, pH and Ka1 by

equation (40).

(40)

Substituting eq. (40) in eq. (39), the mass balance to bicarbonate becomes

(41)

where

.

The timescale of changes in fermentations is sufficiently long such that the reactions involved in the

formation and consumption of bicarbonate are often close to equilibrium [4]

, and therefore it is

assumed that the bicarbonate is in equilibrium with the dissolved CO2 in the beginning of the stop-phase. The

same will not be assumed for the stop-phase, since here no CO2 is removed from the flask, and as such its

concentration in the liquid will increase at a higher rate. The starting value for solving the equation is then

calculated as the starting value for [CO2], multiplied by

. The pH value is measured offline in

normal shake flasks running parallel to the main experiment, and is assumed to remain constant throughout

the stop-phase.

23

The model equations are resumed in table 2.

Table 2 - Model equations with respective initial values

Equation Initial value

-

-

Figure 8 shows a scheme of the phenomena described by the model.

CER

CO2 (l)

pCO2

CTR KLaCO2 pCO2,sensor

τsensor Signal (V)

+ OH- HCO3-

k2

k-2

H++HCO3-

k1

k*-1

CO2 sensor

Fig. 8 - Phenomena captured by the model.

24

3. Materials and Methods

3.1. Characterization of the NDIR sensors

The CO2 sensors used in this work are of the model MSH-P-CO2, produced by Dynament (Derbyshire,

UK). The characterization of the sensors is relevant for studying important features such as signal drift, effect of

shaking on the output signal noise, sensor delay and linearity of the signal. An extensive characterization of the

sensors was done by Hansen [37]; however, the sensors used in this work had a new firmware version and, at a

first approach, presented higher signal noise than the ones used by Hansen, and so it was necessary to some

testing to better understand how this difference could affect the performance.

3.1.1. Effect of the shaking frequency on the output signal

To evaluate the effect of the shaking frequency on the output voltage, a series of sensors were

attached to the flasks and these were placed on a RAMOS device, which in turn was secured onto an orbital

shaker (Kühner AG, Birsfelden, Switzerland). The sensor data was acquired with the RAMOS software,version 3.

The shaking frequency was increased stepwise, from 300 to 360 rpm, with a shaking diameter of 5 cm, and no

gas was fed to the flasks. This experiment was carried out at room temperature. A total of seventeen sensors

were tested. From the seventeen new sensors tested, seven with the smoothest signal were chosen for the

ensuing work, as well as one of the sensors used by Hansen (hereby referred to as “old sensor”, as opposed to

the “new sensors”).

3.1.2. Linearity of pCO2 vs output signal

The next step was to assess the linear relationship of pCO2 vs output signal. The old sensor and two

new sensors were placed in flasks and connected to a RAMOS device. Using two mass flow controllers (MFC),

four different gas mixes of increasing percentage of CO2 are obtained, consisting of varied proportions of air

(0.038% of CO2) and a 4.93% CO2/air mix. These were fed to each flask at a flow of 33.3 mL.min-1

(100 mL.min-1

total). The experiment starts with 100% air being flushed into the flasks (which corresponds to 0.038% of CO2

or 3.8 x 10-4

atm of pCO2). After getting a stable signal from the sensors, the set-point of the MFCs is changed

such that a mixture with 0.0199 atm of pCO2 is obtained, and so on for the other two points (0.0299 and 0.0493

atm). The output flow given by the MFCs in response to the input values were previously determined with a

soap film flowmeter.

25

MFC

MFC

Air/CO2 mix, 4.93% CO2

Air, 0.038% CO2

Gas mixFlow=100 mL/min

Flow=33 mL/min

Fig. 9 - Experimental scheme used for assessing the linearity of the IR sensors

3.1.3. Calibration curves and sensor dynamics

In the RAMOS device used in this work, the sensors are plugged into a circuit board that, besides

supplying the 5 volts needed to power them, also transmits the signal to an ADAM module that in turn

digitalizes and transmits the signal to the computer. For unknown reasons, possibly inherent to the circuit

board, the sensors showed different offset values, and so it was necessary to determine the calibration curve

for each sensor. This calibration curve is needed to convert the raw signal registered by the RAMOS software to

pCO2. Since pCO2 and the output signal were found to be linearly proportional, a good estimate for the

calibration curves can be obtained from two points.

To obtain calibration curves and to study the step response of the sensors, a special device was

assembled. In order to eliminate the mixing effects that can occur if a step increase of pCO2 is applied to a flask,

each sensor was attached to a support with a very small volume, through which the gas sample is flushed. An

O-ring between the sensor and the sampled gas ensures that no external air enters the sensor. The supports

were fixated onto an aluminum base. The gas sample flows through a valve and its flow is then adjusted to 80

mL.min-1

by a mass flow controller. Afterwards, it flows through an eight-way splitter, directing the gas to eight

capillaries of the same length that feed it to the supports holding the sensors. These are connected to the same

electronic parts as in a RAMOS device, which allow the collection of data.

Fig. 10 - Experimental set-up for calibrating the sensors and calculating the time constant

26

Firstly, air (0.038% CO2) was flushed through the supports. After constant reads were obtained from

the sensor, the valve was closed and simultaneously a valve that allowed the flow of an air/CO2 mix (4.93%

CO2) was opened. This caused the signal of the sensors to go up, stabilizing after some time. The points for

calibration were obtained after waiting for the stabilization of the signal. This experiment was run at room

temperature.

With the calibration curves for each sensor, the data produced in the step experiment was converted

from volts to atmospheres of pCO2. Thus, the gain, K (from eq. (27)), of the system is 1 (an increase of a certain

amount of pCO2 in the fed gas is translated into an equal increase in the pCO2 calculated from the signal) and

the step input is 4.892 x 10-2

atm (the pCO2 is increased from 3.8 x 10-4

atm to 4.93 x 10-2

atm, the step size is

given by the difference). A function of the form given by eq. (29) with these parameters was fitted to each

sensor’s step response with the Solver from Microsoft Excel, using the time constant as the fitting parameter.

3.1.4. Effect of different sensor positions on the output signal

As will be discussed in the results section, the sensors showed higher noise for increasing shaking

frequencies, showing oscillations of higher magnitude at 360 rpm for every sensor. To gain more insight on the

nature of this behavior, two sensors were placed on the same supports used for determining the calibration

curves. The supports were then attached to the same device used in the latter experiment, but three different

positions were studied. As can be seen in fig. 11 (adapted from [38]), the light bulb filament is positioned

perpendicularly to the wall of the sensor housing. This was confirmed by opening one sensor.

Fig. 11 - Cutaway drawing of the sensor, evidencing the position of the IR light bulb's filament inside the sensor housing (adapted from [39]).

Laying a support on its side, it was possible to attach the sensor in such a way that the light bulb

filament remains parallel or perpendicular to the base. The third position that was studied was with the sensor

standing upright. The device was fixated onto an orbital shaker with a shaking diameter of 2.5 cm, and the

shaking frequency was increased stepwise from 340 to 370 rpm. This assay was run at 303 K. Figure 12 shows a

schematic drawing of these positions.

27

Fig. 12 - Side view of the three different positions tested for their effect in signal noise.

3.2. Fermentation examples

E. coli BL21 pRSet eYFP-IL6 and E. coli JM109 were used to study the applicability of the model and to

investigate the effect of different gas outlet configurations.

3.2.1. Growth media

E. coli BL21 pRSet eYFP-IL6 was grown on phosphate-buffered TB and TB-glucose media, while the

cultivation of E. coli JM109 was carried out in LB-glycerol media. The media were prepared with yeast extract,

tryptone, KH2PO4, K2HPO4, glycerol and glucose (Carl Roth GmbH, Karlsruhe, Germany), with the concentrations

(g.L-1

) described in table 3. The formulations for these media were obtained from the work of Losen [38].

Table 3 - Composition of the growth media used in the fermentation assays. The concentrations are expressed in g.L-1

.

Components TB TB-glucose LB-glycerol

Yeast extract 24 24 5

Tryptone 12 12 10

Glucose - 5 -

Glycerol 5 - 10

KH2PO4 2.31 2.31 2.31

K2HPO4 12.54 12.54 12.54

The media were autoclaved for 20 minutes at 121oC. To avoid darkening the medium due to Maillard

reactions during autoclaving, two different solutions were prepared for TB-glucose, one with 10 g/L glucose

and one with double the concentration of all the other reagents. For TB and TB-glucose, the pH was close to 7

without any adjustments. The pH of the LB-glycerol medium was adjusted to 7 with a concentrated solution of

HCl.

3.2.2 Culture conditions

All of the fermentations in this work were carried out at 310 K, on orbital shakers (Kühner AG,

Birsfelden, Switzerland) with a shaking diameter of 5 cm. In RAMOS experiments, the flasks were flushed with

28

air at a flow of 0.6 L.min-1

per flask during the rinsing phases, and with 3.6 mL.min-1

during the high flow

phases. The length of each phase is in table 4.

Table 4 - Length of the different phases of the measuring cycle

Phase Length (s)

High-Flow Phase (Phase 1) 54

Low-Flow Phase (Phase 2) 1500

Valve-stop Phase (Phase 3) 60

Stop-flow phase (Phase 4) 300

It should be noted that these time intervals are defined by the user in the RAMOS software. The stop-

phase described before is actually composed by phases 3 and 4, with the defined length of phase 4 being the

total length of the stop-phase.

Respiratory activity of E. coli BL21 pRSet eYFP-IL6 in TB and TB-glucose media

Since glucose and glycerol have different typical respiratory quotients (1.0 and 0.75 respectively) [6],

this parameter will be used as an indicator of the suitability of the model. Two RAMOS flasks with a total

volume of 250 mL were used for making the pre-cultures. The flasks were filled with 10 mL of TB or TB-glucose

medium, supplemented with 100 g.L-1

of ampicillin. Each flask was then inoculated with 100 L of a

cryoculture of E. coli BL21 pRSet eYFP-IL6 that had been grown on TB medium. The flasks were shaken at 350

rpm, and the oxygen transfer rate of the pre-cultures was monitored with an in-house built RAMOS device. The

cultures were stopped after the OTR reached around 40 mM.h-1

. Then, suitable volumes of TB and TB-glucose

supplemented with 100 g.L-1

of ampicillin were inoculated with the corresponding pre-culture, at an inoculum

rate of 1%. A total of eight RAMOS flasks and twenty normal 250 mL shake flasks were filled with 10 mL of

inoculated broth each, half of the flasks with TB and the other half with TB-glucose. The fermentation was

performed for 10 hours at a shaking frequency of 340 rpm, 10 rpm less than the pre-culture, in order to obtain

a smoother signal from the CO2 sensors. Monitoring of the OTR and logging of the CO2 sensors signal was done

with a RAMOS device. The logging frequency was set to 60 measurements per minute. The pH values were

obtained by offline measurement with a pH electrode in the normal shake flasks, with each flask being used for

a single measurement.

Respiratory activity of E. coli JM109 in LB-glycerol media

The methods used for the cultivation of E. coli JM109 in LB-glycerol were similar, except that the

fermentation was run for 25 hours. The logging frequency was set to 30 measurements per minute.

29

3.3. Effect of different gas outlet configurations on the measured respiratory activity

One of the major drawbacks of calculating the CTR with differential pressure sensors is that this

method requires the flasks to be gas-tight for the calculated value to be relevant. The need for gas-tightness

increases the production cost of the flasks; the IR sensor method does not require this specification.

Furthermore, removing the outlet valve could also reduce the device’s overall cost. However, this could still

have some implications in the measured respiratory activity. For example, when the transfer quotient is smaller

than 1, it is plausible to think that external air could enter the flask by convective and diffusive mechanisms,

affecting the measured OTR; conversely, when the TQ is larger than one, CO2 could exit the flask, reducing its

partial pressure and thusly affecting the measured CTR.

The flask’s gas outlet is filled with cotton and is equipped with a screw cap that holds in place a

perforated stainless steel piece, with a flat seal underneath. The gas flows out of the flask, through the

perforated steel piece and into a gas-tight tube that is connected to the outlet valve (fig. 13). To understand

the effect of different gas outlet configurations in the absence of an outlet valve, E. coli pRSet eYFP-IL6 was

grown in TB-glucose medium, supplemented with 100 g.L-1

of ampicillin and the differences in respiratory

activity were evaluated. The culture conditions were the same as for the fermentations described in section

3.2. To minimize differences related to the cotton plug, 0.1 g of cotton was weighed for each plug, and carefully

stuffed into the flask’s outlet such that the same compaction could be obtained. Four different configurations

were tested (two flasks for each):

-Config. A: normal configuration;

-Config. B: outlet tubing connected to an open outlet valve;

-Config. C: outlet tubing removed;

-Config. D: stainless steel piece removed.

A

B

DC

EF

Fig. 13 - Schematic illustration of the gas outlet on a RAMOS flask. A - outlet of the flask, filled with a cotton plug; B - screw cap; C - stainless steel piece; D - o-ring; E – gas tight tubing; F - outlet valve.

30

3.4. Automated calculation of CTR and CER

In order to quickly process the large amount of data generated by the RAMOS software and perform

CER and CTR calculations, a program was created in MATLAB R2011b (MathWorks, Massachusetts, USA). The

program begins by asking for the measurement data file, which contains the raw signal from all the sensors.

The function SortCO2 then extracts the data belonging to the CO2 sensors for each rinse phase and each stop-

phase (phase 2 and phases 3 and 4 respectively, as defined in the RAMOS software), converting the raw signal

into pCO2 with the sensor-specific calibration curves. The data from the stop-phases and the rinse-phases are

stored in two different variables. The program then requires the user to define the operational parameters VL

(L), Vg (L), T (K), d0 (cm), N (rpm), Fout (L.h-1

) and pH. In the next phase, the calculation of the CER and CTR starts,

beginning with the first sensor and first measuring cycle until the last measuring cycle from the first sensor,

proceeding to the second sensor and its first measuring cycle and so on. The rinse phase data and the sensor

time constant are used as inputs to the function RPcalc, returning the model parameter

after

optimization with the non-linear least squares solver lsqnonlin from Matlab. The function ModelOptim is used

to fit eq. (29) to the experimental data, taking the operational parameters and stop phase data as inputs and

returning the fitting parameters b and c upon optimization with lsqnonlin. These parameters are inserted into

the function ModelCER, along with the pH and the other operational parameters, returning the CTR and CER.

The program ends upon reaching the last measuring cycle of the last sensor. The parameters used by the model

and respective values are listed in table 5. In figure 14, a flow chart of the program is depicted.

Table 5 - Parameters used in the computation of the CER and CTR

Parameter Symbol Value

Temperature T 310 K

Time constant 0.0237h (new sensors);

0.0366h (old sensors)

Gas flow Fout 0.6 L.h-1

Shaking frequency N 340 rpm

Shaking diameter d0 5 cm

Flask diameter d 8 cm

Liquid volume VL 10 mL

Headspace volume Vg Varies with flask

Volumetric mass transfer coefficient KLaCO2

273 h-1

Henry’s law coefficient at 310 K [43] hCO2

27.2 mM.atm-1

Reaction rates at 310 K [13] k1 5.030 x 10-2

h-1

k*-1 1.094 x 109 M

-1.h

-1

k-2 6.346 h-1

k2 1.117 x 108 M

-1.h

-1

First dissociation constant of carbonic acid

at 310 K [13] Ka1 10

-3.581 M

31

Function/Process

Data

Manual Input

Decision

Shape key

SortCO2

Rinse-phase Measurements

Stop-phase Measurements

RAMOS Measurement data

RPcalc

lsqnonlin

dPCO2,rinse/dt

Operational parameters

ModelOptim

lsqnonlin

Parameters b and c

CER and CTR

Last Cycle?

Yes

Last Sensor?

Compilationof all CER and CTR values

Yes

Noa=a+1

No n=n+1a=1

Retrieve data from n-th, sensor, a-th

cycle

Retrieve data from n-th, sensor, a-th

cycle

Rinse-phase data

Stop-phase data

ModelCER

Fig. 14 - Flowchart of the automated calculation of CTR and CER

32

4. Results and discussion

4.1. Characterization of the NDIR sensors

4.1.1. Effect of shaking frequency on the output signal

The effect of the shaking frequency on the output of seventeen new sensors was examined. The new

sensors showed higher noise levels than the sensors used by Hansen [37], increasing with the shaking

frequency. For simplification matters, only the data for three sensors are shown here.

Fig. 15 - Effect of different shaking frequencies in the signal of three selected sensors. T=298 K, d0=5 cm, pCO20.

After inquiring about this behavior, the manufacturer suggested some changes in the firmware

definitions in order to reduce the noise. The experiment was repeated with the new definitions and there was

indeed an improvement, but not for all of the sensors, as can be seen in figure 16: sensors A and B are

smoother, but sensor C seems almost as noisy, if not noisier. For sensors B and C the signal may seem smooth

but may actually be noisier since a resolution of three decimal digits was used, instead of the maximum

resolution of four digits. It should also be noted that despite being pre-calibrated, the sensors show different

offset values. It was noticed that at 360 rpm, all the sensors showed large oscillations.

290

300

310

320

330

340

350

360

370

0.4

0.405

0.41

0.415

0.42

0.425

0.43

0.435

0 0.2 0.4 0.6 0.8 1

Shak

ing

Fre

qu

en

cy [

RP

M]

Ou

tpu

t si

gnal

[V

]

Time [h]

Sensor 1

Sensor 2

Sensor 3

Shaking frequency

Sensor A

Sensor B

Sensor C

33

Fig. 16 - Effect of different shaking frequencies in the signal of three selected sensors, with new filter definitions. T=298

K, d0=5 cm, pCO20.

A total of seventeen new sensors were tested with the new definitions. A set consisting of one old

sensor and seven of the new sensors with the smoothest output signal were chosen for the following work.

4.1.2. Linearity of output signal vs pCO2

The sensors were shown to provide a linear response to different pCO2 values (fig. 17). The mass flow

controllers add some uncertainty to the actual amount of CO2 and/or total flow; it was relatively hard to set the

MFCs to the previously determined values, and some small drifting in the output given at a certain input value

was noticeable after prolonged periods.

Fig. 17 - Three sensors showing a linear response to increasing carbon dioxide partial pressures. T=303 K, Flow=33 mL.min

-1, d0=5 cm, N=300 rpm.

4.1.3. Calibration curves and sensor dynamics

A set of eight sensors (one old and seven new) were exposed to a step increase of pCO2 from 3.8x10-4

to 4.93x10-2

atm, showing different responses in the produced output signal, as can be seen in figure 18.

290

300

310

320

330

340

350

360

370

0.4

0.405

0.41

0.415

0.42

0.425

0.43

0.435

0 0.2 0.4 0.6 0.8 1

Shak

ing

Fre

qu

en

cy [

RP

M]

Ou

tpu

t si

gnal

[V

]

Time [h]

Sensor 1

Sensor 2

Sensor 3

Shaking frequency

R² = 0.9972

R² = 0.9992

R² = 0.9999

0

0.4

0.8

1.2

1.6

2

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05

Ou

tpu

t Si

gnal

[V

]

Partial pressure of CO2 [atm]

Sensor 1

Sensor 2

Sensor 3

Sensor A

Sensor B

Sensor C

34

Fig. 18 - Response of eight sensors to a step increase from 3.8x10-4

to 4.93x10-2

atm of pCO2. T=303K, flow=10 mL.min-1

.

Due to this behavior, individual calibration curves have to be calculated for each sensor. A calibration

curve of the type

(42)

is applied, where KCO2 is the slope of the curve (atm.V-1

), Vsensor is the output signal (V) and pCO2,V0 (atm) is the

theoretical pCO2 when the sensor output is equal to zero. The parameters for each sensor can be found in table

6.

Table 6 - Calibration curve parameters.

Sensor 1 2 3 4 5 6 7 8

KCO2.102 (atm.V

-1) 3.350 3.571 3.709 3.511 3.501 3.368 3.917 3.340

pCO2,V0.102 (atm) -1.339 -1.459 -1.503 -1.429 -1.441 -1.392 -1.610 -1.372

With the calibration curves, the signal was converted to pCO2, and the sensor time constant () was

calculated. Figure 19 shows the fitting for a new sensor and an old sensor. The new sensors showed a smaller

time constant than the old sensor. The calculated time constant for the seven new sensors was 0.0237 hours

in average, with a standard deviation of 0.0015 hours, and for the old sensor was 0.0336 hours; the value for

the old sensor is in accordance with the one obtained by Hansen [37].

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 0.1 0.2 0.3 0.4 0.5

Ou

tpu

t Si

gnal

[V

]

Time [h]

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Sensor 5

Sensor 6

Sensor 7

Sensor 8

35

Fig. 19 – Step response of one old sensor and one new sensor, and respective fitting curves. Step=0.0489 atm, T=298 K, Flow=0.6 L.h

-1.

4.1.4. Effect of different sensor positions on the output signal

The sensors showed particularly high noise levels when shaken at 360 rpm. To ascertain whether this

was a physical effect caused by the shaking of internal components, the effect of three different positions of

the light bulb filament was studied with two sensors.

Fig. 20 – Effect of different shaking frequencies on the signal of two sensors, positioned with the light bulb filament parallel to the ground. T=303 K, d0=2.5 cm.

0.00

0.01

0.02

0.03

0.04

0.05

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

pC

O2

[atm

]

Time [h]

Sensor 1 (old sensor)

Sensor 10 (new sensor)

Step

Sensor 1 (old sensor), fitting

Sensor 10 (new sensor), fitting

335

340

345

350

355

360

365

370

375

0.417

0.419

0.421

0.423

0.425

0.427

0.429

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Sign

al o

utp

ut

[V]

Time [h]

Sensor 1

Sensor 2

Shaking frequency

36

Fig. 21 – Effect of different shaking frequencies on the signal of two sensors, in an upright position. T=303 K, d0=2.5 cm.

Fig. 22 – Effect of different shaking frequencies on the signal of two sensors, positioned with the light bulb filament perpendicular to the ground. T=303 K, d0=2.5 cm.

To avoid misinterpretation, the graphs are shown within the same time and signal ranges (0.7 hours

and 0.012 volts, respectively). There were no evident differences found between the behavior of the sensors in

an upright position and with the filament parallel to the ground, except for the larger amplitude of oscillation in

the upright position for a shaking frequency of 360 rpm. The largest difference was found for the case where

the filament is perpendicular to the ground: the frequency and amplitude of the oscillation at 360 rpm are

much smaller. The decaying of the signal that is observed is probably due to the warming up time of the

sensors.

335

340

345

350

355

360

365

370

375

0.415

0.417

0.419

0.421

0.423

0.425

0.427

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Sign

al o

utp

ut

[V]

Time [h]

Sensor 1

Sensor 2

Shaking frequency

335

340

345

350

355

360

365

370

375

0.433

0.435

0.437

0.439

0.441

0.443

0.445

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Sign

al o

utp

ut

[V]

Time [h]

Sensor 1

Sensor 2

Shaking frequency

37

When the filament is parallel to the ground or the sensor is in an upright position, it can be

hypothesized that the shaking mechanically affects the filament in a similar fashion; the oscillation could be

caused by the filament compressing (fig., somehow changing the intensity of light that reaches the sensors.

Fig. 23 – Hypothetical behavior of the light bulb filament when the sensor is shaken in an upright position (sensor seen from above).

However, following this thinking, if the filament is perpendicular to the ground, the shaking does not

force the filament to compress. The oscillation that can still be seen in this position could be due to the

filament not being completely perpendicular. Although not conclusive, these results do suggest a relationship

between the observed effect of shaking at 360 rpm and the way in which the light bulb is positioned; this

knowledge can be used to reduce sensor noise in future RAMOS models.

4.2 Mathematical model: examples, simulations, and possible validation methods

4.2.1. Examples

The modeling of two stop-phases from the cultivation of E. coli BL21 pRSet eYFP-IL6 in TB medium is

presented (figs. 24 and 25). The first stop-phase is from the exponential growth phase, while the second is from

the end of the stationary phase.

The model seems to fit the data well. In the second stop-phase, the calculated initial value for pCO2 is

lower than the initial value for pCO2,sensor because the signal was dropping before the stop-phase (due to

more CO2 being removed than the amount being transferred from the liquid) and the time constant causes a

discrepancy between these two; so, naturally, the pCO2 in the headspace was lower than what the sensor

indicated at the beginning of the stop-phase. This discrepancy is also observed in the first stop-phase.

38

Fig. 24 – pCO2 during a stop-phase in the exponential growth phase, at 2.5 hours in. E. coli BL21 pRSet eYFP-IL6 in TB medium, T=310 K, N=340 rpm, d0=5 cm, VL=0.010 L, Vg=0.271 L, CTR=46 mM.h

-1, CER=53 mM.h

-1. Blue line – sensor data

converted to pCO2; green line – model fitting of the experimental data; red line – Partial pressure of CO2

Fig. 25 - pCO2 during a stop-phase in the end of the stationary phase, at 5.5 hours in. E. coli BL21 pRSet eYFP-IL6 in TB medium, T=310 K, N=340 rpm, d0=5 cm, VL=0.010 L, Vg=0.271 L, CTR=36 mM.h

-1, CER=46 mM.h

-1. Blue line – sensor data

converted to pCO2; green line – model fitting of the experimental data; red line – Partial pressure of CO2.

The profiles of dissolved carbon dioxide and bicarbonate are graphically represented in figures 26 and

27. The bicarbonate is calculated from the pH and dissolved CO2 values, which in turn are obtained from the

pCO2 values. The pH was measured in normal shake flasks running in parallel, and is assumed to be constant

throughout the stop-phase. The dissolved CO2 is within the range given by Royce and Thornhill [12] for the

respective pCO2 values.

0.012

0.013

0.014

0.015

0.016

0.017

0.018

0.019

0.02

0 0.02 0.04 0.06 0.08 0.1

pC

O2

[atm

]

Time [h]

pCO2, sensor

pCO2

pCO2, sensor, fitting

0.0202

0.0203

0.0204

0.0205

0.0206

0.0207

0.0208

0.0209

0.021

0.0211

0.0212

0 0.02 0.04 0.06 0.08 0.1

pC

O2

[at

m]

Time [h]

pCO2, sensor

pCO2

pCO2, sensor, fitting

39

Fig. 26 - Dissolved CO2 and bicarbonate during a stop-phase in the exponential growth phase, at 2.5 hours in. E. coli BL21

pRSet eYFP-IL6 in TB medium, T=310 K, N=340 rpm, d0=5 cm, VL=0.010 L, Vg=0.271 L, pH=7.15, CTR=46 mM.h-1, CER=53

mM.h-1

.

Fig. 27 - Dissolved CO2 and bicarbonate during a stop-phase in the end of the stationary phase, at 5.5 hours in. E. coli

BL21 pRSet eYFP-IL6 in TB medium, T=310 K, N=340 rpm, d0=5 cm, VL=0.010 L, Vg=0.271 L, pH=7.65, CTR=36 mM.h-1,

CER=46 mM.h-1

.

4.2.2. Effect of the pH on the predicted CER

To understand the effect of the pH on the CER predicted by the model, the bicarbonate concentration

during a stop-phase was simulated for constant pH values ranging from 6 to 8. The effect of a shifting pH was

also evaluated. The stop-phase used in this example is from the cultivation of E. coli pRSet eYFP-IL6 in TB-

glucose medium, 3 hours into the fermentation.

3.5

3.6

3.7

3.8

3.9

4.0

4.1

4.2

4.3

4.4

4.5

0.55

0.57

0.59

0.61

0.63

0.65

0.67

0.69

0.71

0.73

0.75

0 0.02 0.04 0.06 0.08 0.1

Bic

arb

on

ate

[m

M]

Dis

solv

ed

CO

2

[mM

]

Time [h]

CO2

Bicarbonate

10.60

10.65

10.70

10.75

10.80

10.85

10.90

10.95

11.00

0.58

0.585

0.59

0.595

0.6

0.605

0.61

0.615

0.62

0 0.02 0.04 0.06 0.08 0.1

Bic

arb

on

ate

[m

M]

Dis

solv

ed

CO

2

[mM

]

Time (h)

CO2

Bicarbonate

40

Fig. 28 - pCO2 and dissolved CO2 concentration during a stop-phase at 3 hours into the fermentation. E. coli BL21 pRSet eYFP-IL6 in TB-glucose medium, T=310 K, N=340 rpm, d0=5 cm, VL=0.010 L, Vg=0.281 L.

Constant pH

The bicarbonate concentration profiles for different pH values are depicted in fig. 29. For viewing

purposes, each profile was subtracted of its initial value, since this varies significantly with the pH.

Fig. 29 - Predicted bicarbonate concentrations for different pH values. E. coli BL21 pRSet eYFP-IL6 in TB-glucose medium, T=310 K, N=340 rpm, d0=5 cm, VL=0.010 L, Vg=0.281 L.

The model calculates the CER as the sum of the CTR and the variation of carbon dioxide and

bicarbonate concentrations (eq. (30)). As can be seen in fig. 30, the CER predicted by the model is highly

dependent on the pH.

0.85

0.9

0.95

1

1.05

1.1

0.02

0.021

0.022

0.023

0.024

0.025

0.026

0.027

0.028

0.029

0 0.02 0.04 0.06 0.08 0.1

Dis

solv

ed

CO

2 [

mM

]

pC

O2

[at

m]

Time [h]

pCO2, sensor

pCO2

pCO2, sensor, fitting

Dissolved CO2

0

0.5

1

1.5

2

2.5

3

3.5

0 0.02 0.04 0.06 0.08 0.1

[HC

O3

- ]-[

HC

O3- ]

0

[mM

]

Time [h]

pH 6

pH 6.5

pH 7

pH 7.5

pH 8

41

Fig. 30 - Predicted CER for different pH values. E. coli BL21 pRSet eYFP-IL6 in TB-glucose medium, time=3 hours, T=310 K, N=340 rpm, d0=5 cm, VL=0.010 L, Vg=0.281 L.

Shifting pH

The pH is assumed to be constant; however, the accumulation of dissolved carbon dioxide in the liquid

media during the stop-phase, and the subsequent formation and dissociation of carbonic acid can cause the pH

to decrease, especially when the buffer capacity of the medium has been exceeded. Measuring the pH in

normal shake flasks running in parallel does not take this effect into account. An increase in [H+] would limit the

formation of bicarbonate as predicted by the model (eq. (41)), therefore computing a lower CER value;

conversely, a decrease in [H+] would result in a higher CER. The effect of constant rates of pH change in the

bicarbonate concentration and in the CER is shown in figures 31 and 32, respectively.

Fig. 31 - Bicarbonate concentration during a stop-phase with constant rates of change in pH. Initial pH is 7.5.

80

85

90

95

100

105

110

115

120

125

5.5 6 6.5 7 7.5 8 8.5

CER

[m

M.h

-1]

pH [-]

11

11.5

12

12.5

13

13.5

14

14.5

15

15.5

0 0.02 0.04 0.06 0.08 0.1

[HC

O3- ]

-[H

CO

3- ]0

[m

M]

Time [h]

d(pH)/dt = -1/h

d(pH)/dt = -0.5/h

d(pH)/dt = -0.1/h

d(pH)/dt = 0.1/h

d(pH)/dt = 0.5/h

d(pH)/dt = 1/h

42

Fig. 32 - Predicted CER for constant rates of change in pH. E. coli BL21 pRSet eYFP-IL6 in TB-glucose medium. Initial pH=7.5, time=3 hours, T=310 K, N=340 rpm, d0=5 cm, VL=0.010 L, Vg=0.281 L.

Many factors can affect the pH of the medium, and as such it is difficult to predict how the pH behaves

during a stop-phase solely from measurements performed in normal shake flasks running in parallel. A way to

overcome this issue would be to use pH sensitive sensor spots, as have Scheidle et al [32] for example.

4.2.3 Possible validation methods

The small volume of the flasks limits the validation strategies that can be employed. In the works of

Royce [4], Spérandio [5] and Jonge [14] similar methods were employed in lab-scale stirred fermenters. Quasi-

steady state conditions are achieved, such that the CER is equal to the CTR, and then the validation of the

model is done by studying the response of the CTR and the pH to perturbations in the input variables. This

would be extremely difficult or even impossible to do in a RAMOS system due to the size and geometry of the

flasks.

Neeleman et al [22] employed a different strategy. The CER was simulated by adding known amounts

of a bicarbonate solution to cell-free medium in a fermenter, and the model parameters were obtained by

measuring the CTR and the pH. The model was then able to predict the lumped concentration of CO2 and

bicarbonate based on the CTR and pH. A similar strategy could be used in this case, either through directly

pumping a solution of known concentration of bicarbonate to the flask or using some sort of slow-release

device inside the flask, in conjunction with online pH measurement.

Another option would be to establish a mass balance to carbon with the aid of liquid sample analysis

to measure biomass, dissolved sugars and known fermentation byproducts. The dissolved CO2 could be

measured either offline, using a Biolyzer system, or online, with dissolved CO2 sensor spots [31].

80

85

90

95

100

105

110

115

120

125

130

-1.5 -1 -0.5 0 0.5 1 1.5

CER

[m

M.h

-1]

d(pH)/dt [h-1]

43

4.3. Fermentation examples

To verify the applicability of the model, two cultivation essays were performed in a RAMOS device,

with flasks equipped with the CO2 sensors.

4.3.1. E. coli pRSet eYFP-IL6 in buffered TB and TB-Glucose media

In the first essay, E. coli pRSet eYFP-IL6 was grown for 10 hours in two different TB-based media, with

one containing glycerol and the other containing glucose (referred to as TB and TB-glucose, respectively) as

carbon sources. The experiment was carried out at 37oC and a shaking frequency of 340 rpm. The CER and CTR

values were calculated from the CO2 sensors’ readings using the program described in section 3.3. The pH

measurements were made with normal shake flasks that were running in parallel with the RAMOS experiment.

Since the pH measurement was done every hour and the stop-phases occurred every half hour, the pH values

in between were interpolated for the calculation of the CER. At around 6.5 hours into the fermentation, the

RAMOS device had a problem (most likely a short circuit) and the measurement was halted. Only about 1.5

hours later was it possible to resume the assay. This interruption may have hurt the microbial activity, since the

device was removed from the fermentation chamber during this hiatus, resulting in a lack of oxygenation.

Figures 32 and 33 show the OTR, the CER, the CTR-S (CTR calculated with the IR sensors) and the CTR-P (CTR

obtained from the differential pressure and OTR) for these fermentations, as well as the pH readings.

Fig. 33 – OTR, CER, CTR-S and CTR-P of a culture of E. coli pRSet eYFP-IL6 in TB-glucose medium. T=310 K, N=340 rpm, d0=5 cm, VL=0.010 L, Vg=0.270 L.

6

6.5

7

7.5

8

8.5

9

0

10

20

30

40

50

60

70

80

90

100

0 2 4 6 8 10 12

pH

OTR

, CTR

an

d C

ER [

mM

.h-1

]

Time [h]

OTR

CER

CTR-S

CTR-P

pH

44

Fig. 34 - OTR, CER, CTR-S and CTR-P of a culture of E. coli pRSet eYFP-IL6 in TB-glucose medium. T=310 K, N=340 rpm, d0=5 cm, VL=0.010 L, Vg=0.282 L.

Although not so evident from the OTR profile, diauxic growth can be observed from the CTR and CER

profiles, indicating a change in substrate, in conjunction with a change in pH evolution. This could be caused by

what is known as the acetate metabolism overflow. High growth rate aerobic E. coli cultivations often result in

the excretion of acetate, acidifying the medium. This phenomenon was found to be caused by carbon

catabolite repression of the Acetil-CoA synthetase [45]. When the primary carbon source is exhausted, the cell

starts to consume acetate if no other more readily metabolized substrates are available [37]. The consumption

of acetate causes the medium pH to rise again. After completely exhausting carbohydrate substrates, catabolic

degradation of aminoacids becomes predominant, with ammonia accumulating in the broth as a result, further

increasing the pH [46]. In the work of Hansen [37], this particular strain was grown in Wilms-MOPS medium

and this mechanism was observed.

Another relevant feature that can be observed is the discrepancy between the two methods for CTR

calculation. The IR sensor method seems much more sensitive to small changes; for example, at the 3.5 hour

point in the TB-glucose medium, there is a very subtle drop in CTR-P, while the CTR-S shows a very pronounced

decrease. A large difference is also noticeable when the stationary phase is reaching the end, especially for the

TB-glucose medium. For example, at 5.5h, CTR-P is 27 mM.h-1

and CTR-S is only 7 mM.h-1

.

The Respiratory (RQ) and Transfer Quotients, obtained with both pressure differential and IR sensor

methods (TQ-S and TQ-P) were calculated (fig.35). The RQ values do not correspond exactly to the typical RQ

values provided in table 1; however, in both situations there is a visible change in RQ around 3h and 4h for TB-

glucose and TB respectively, suggesting a change in carbon source. In the TB-glucose medium, the RQ is

6

6.5

7

7.5

8

8.5

9

0

10

20

30

40

50

60

70

80

90

100

0 2 4 6 8 10 12

pH

OTR

, CTR

an

d C

ER [

mM

.h-1

]

Time [h]

OTR

CER

CTR-S

CTR-P

pH

45

relatively constant around 1.4 decaying to 1.2 after the substrate shift at 3.5 hours, which is in agreement with

the change from glucose to acetate, with typical RQ values of 1 and 0.8 respectively; in the medium containing

glycerol, the RQ increases slightly from ca. 1 to 1.2 four hours in, which is also in accordance with the substrate

shift from glycerol to acetate (typical RQ values of 0.75 and 0.80 respectively).

Fig. 35 – RQ (blue diamonds), TQ-S (red squares) and TQ-P (green triangles) for E. coli pRSet eYFP-IL6 grown in TB-glucose (left) and TB (right).

4.3.2 E. coli JM109 in LB-glycerol medium

In the second assay, the E. coli JM109 strain was cultivated in a buffered LB-based medium, with a

glycerol concentration of 10 g.L-1

. The pH was measured offline, remaining constant around pH 7 throughout

the whole fermentation assay. The time profiles for OTR, CTR-S, CTR-P and CER are shown in fig.36.

Fig. 36 – Measured respiratory activity (OTR, CER, CTR-P, CTR-S) of E. coli JM109 gown on LB-glycerol media. T=310 K, N=340 rpm, d0=5 cm, VL=0.01 L, Vg=0.270 L.

0

0.3

0.6

0.9

1.2

1.5

1.8

2.1

2.4

0 2 4 6 8 10 12 Time [h]

RQ Glucose

TQ Glucose, IR sensor

TQ Glucose, RAMOS

0

0.3

0.6

0.9

1.2

1.5

1.8

2.1

2.4

0 2 4 6 8 10 12 Time [h]

RQ Glycerol

TQ Glycerol, IR sensor

TQ Glycerol, RAMOS

0

5

10

15

20

25

30

35

0 5 10 15 20 25 30

OTR

, CTR

an

d C

ER [

mM

.h-1

]

Time [h]

CTR-P

OTR

CER

CTR-S

46

In this fermentation, there seems to be a combination of diauxic growth and non-carbon substrate

limitation (see fig. 5). Two peaks in respiratory activity appear between 7 and 11 hours, possibly indicating a

substrate shift; afterwards the respiratory activity shows a plateau, pointing to substrate limitation [34]. In the

TB medium, there is a much larger proportion of non-carbon substrates (tryptone and yeast extract) to glycerol

than in the LB-glycerol medium used here, corroborating this hypothesis. Again, there is a large discrepancy

between CTR-S and CTR-P. Looking at the Respiratory and Transfer Quotients (fig. 37), the RQ averages at 0.75

(the typical value for glycerol) during the plateau (10-20h), while the TQ-P values averages at 0.85, suggesting

that the CTR-S could be closer to the real value.

Fig. 37 - RQ ,TQ-S and TQ-P for E. coli JM109 grown in LB-glycerol medium.

4.4. Influence of the gas outlet configuration in the respiratory activity measurement

E. coli pRSet eYFP-IL6 was grown in TB-glucose medium, and the effect of four different gas outlet

configurations in the respiratory activity of the culture was tested:

-Config. A: normal configuration;

-Config. B: outlet tubing connected to an open outlet valve;

-Config. C: outlet tubing removed;

-Config. D: tubing and stainless steel piece removed.

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

0 2 4 6 8 10 12 14 16 18 20 22 24 26

Time [h]

RQ

TQ-S

TQ-P

47

A short circuit in the beginning of the fermentation interrupted the RAMOS measurement, being

resumed at around 2 hours afterwards. The OTR and CTR-P for each flask can be found in fig. 38. Only one plot

for configuration B is shown because one of the O2 sensors had a malfunction. No significant differences were

found between the four different configurations in the OTR.

Fig. 38 - OTR of E. coli pRSet eYFP-IL6 grown in TB-glucose. T=310 K, N=340 rpm, d0=5 cm, VL=0.01 L. Gas outlet configurations: A-normal configuration, B-tubing connected to an open valve, C – tubing removed, D – tubing and

stainless steel piece removed.

As expected, the CTR-P measurement was severely affected for configurations other than A (fig. 39).

Since the calculated pressure differential is near zero, the CTR-P is equal to the OTR for configurations B, C and

D.

Fig. 39 – CTR-P of E. coli pRSet eYFP-IL6 grown in TB-glucose. T=310 K, N=340 rpm, d0=5 cm, VL=0.01 L. Gas outlet configurations: A-normal configuration, B-tubing connected to an open valve, C – tubing removed, D – tubing and

stainless steel piece removed.

0

10

20

30

40

50

60

70

80

0 1 2 3 4 5 6 7 8

OTR

(m

M.h

-1]

Time [h]

A

A

B

C

C

D

D

0

10

20

30

40

50

60

70

80

0 1 2 3 4 5 6 7 8

CTR

[m

M.h

-1]

Time [h]

A

A

B

C

C

D

D

48

As for the CTR-S measurements, while varying significantly from sensor to sensor, no pattern was

found that could tell the differences between configurations (fig. 40). The CTR-S was higher for configuration A

in most of the points, but there are no noticeable differences between the other three configurations that

could point to a conclusion; even between each pair of flasks with the same configuration the CTR values vary.

Therefore, no conclusions can be drawn as to the effect in the CTR-S of the different configurations.

Fig. 40 – CTR-S of E. coli pRSet eYFP-IL6 grown in TB-glucose. T=310 K, N=340 rpm, d0=5 cm, VL=0.01 L. Gas outlet configurations: A-normal configuration, B-tubing connected to an open valve, C – tubing removed, D – tubing and

stainless steel piece removed.

0

10

20

30

40

50

60

70

80

0 1 2 3 4 5 6 7 8

CTR

-S [

mM

.h-1

]

Time [h]

A

A

B

C

C

D

D

49

5. Conclusion and Outlook

In this work, a mathematical model for the Carbon Dioxide Evolution Rate of microbial cultures in a

RAMOS device was developed, with the use of NDIR sensors for pCO2 measurement and offline pH

measurements.

The characterization of the NDIR sensors was carried out to verify the linearity of the signal,

investigate the effect of shaking in the signal noise, calibrate the sensors and determine their time constant.

The effect on the sensor noise for different sensor positions was also investigated, and the best position for

noise reduction at high shaking frequencies was successfully determined

The response of the model to simulated constant and shifting pH was studied, for a set of

experimental data from a stop-phase. In either situation, the CER was significantly affected. Therefore, taking

offline pH measurements and simply assuming a constant value throughout the stop-phase may produce a less

accurate CER; online measurement with pH-sensitive sensor spots would tackle this problem and reduce

uncertainty.

Validation of the model was not carried out; two possible validation strategies were presented here.

One would be to somehow simulate a known CER by adding known amounts of bicarbonate to a flask,

monitoring the pCO2 in the headspace as well as online pH measurement. Another way would be to perform

offline liquid sample analysis to establish a mass balance to carbon.

The effect of removing the gas outlet valve on the measured respiratory activity of an E. coli pRSet

eYFP-IL6 culture was also evaluated. No major differences were noticed in each case for the OTR; in the case of

the CTR no conclusions could be drawn from the data, since high variability within each configuration was

present.

The suitability of the model was tested by monitoring the growth of E. coli pRSet eYFP-IL6 in media

containing either glucose or glycerol as the sole carbohydrate source. The differences in respiratory quotients

indicated that the model was able to provide a good estimate of the CER. However, this estimate can only be as

good as the CTR that can be calculated from the NDIR sensors, and this method showed some discrepancies

with the state-of-the-art pressure differential method, unlike the good agreement between both methods that

Hansen obtained [37]. There was also high variability between the CTR calculated with different sensors in the

same experimental conditions. The high noise of the sensors might have contributed to this situation; also, the

CTR calculation method may have to be ameliorated. Only with a proper CTR measuring method, coupled with

online pH measurement, can the CER be accurately predicted.

50

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