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Modelling, Optimization and Control of Yeast Fermentation

Processes in Food Industry

Anne Richelle

Ph.D. Thesis submitted at the

cole polytechnique de Bruxelles Université libre de Bruxelles and presented on 31th March, 2014

in fulfillment of the requirements for the degree of Docteur en Sciences de l’Ingénieur

Jury members

Pr. Dr. Ir. M. Kinnaert Univeristé Libre de Bruxelles - President Pr. Dr. Ir. F. Debaste Université Libre de Bruxelles - Secretary Pr. Dr. Ir. A. Vande Wouwer Université de Mons

Pr. Dr. Ir. J. Van Impe Katholieke Universiteit Leuven Pr. Dr. J.-M. Sablayrolles INRA Montpellier, France

Pr. Dr. Ir. Ph. Bogaerts Université Libre de Bruxelles - Thesis Advisor

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Chaque porte passée est une fenêtre ouverte sur le reste avenir...

Remerciements

Mes premiers remerciements s’adressent au Fonds pour la formation à la Recherche dans l’Industrie et dans l’Agriculture et au Fonds David & Alice Van Buuren qui ont financé cette thèse de doctorat.

Je tiens également à remercier Coralie Lefebvre, Bernard Genot et Sylvestre Awono, nos collaborateurs industriels de Puratos qui ont contribué à la mise en perspective de ces recherches dans un contexte industriel.

Je tiens à souligner l’investissement des mémorants avec qui j’ai eu l’occasion de travailler sur certaines parties de cette thèse: Sergio Gutiérrez, Nicolas Marquet, Guevork Mikaelian et Martina Tomassini.

Je remercie Jean Louis Van Pee, Laurent Catoire et Serge Torfs pour l’aide technique qu’ils m’ont apportée dans le cadre de la mise en place des in- stallations expérimentales; Laurent Dewasme dont les conseils avisés m’ont permis d’élargir mes réflexions; la Professeure Laurence Van Nedervelde et Roxane Van Heurck pour les relectures de cette thèse; tous les membres du service 3BIO qui ont subi mes blagues à trois francs six sous pendant de nombreuses années et plus particulièrement Nathalie, Danièle, Jean-Marc, Zakaria, Khadija et Marie sans oublier mon cher Alex; et bien évidement tous les amis sur qui j’ai pu compter durant ces cinq dernières années: ils ont largement contribué à mon sourire quotidien!

Je n’aurais jamais pu réaliser cette thèse sans le soutien inconditionnel de ma famille: François, Marie, ma mère et mon père. Je ne saurais jamais assez les remercier d’être toujours là pour moi.

Last but not least, il est celui sans qui rien de tout cela n’aurait pu voir le jour et sans nulle doute ma plus belle rencontre universitaire: le Professeur Philippe Bogaerts. Grâce à son exigence, j’ai acquis des qualités qui m’ont longtemps fait défaut: la rigueur et la patience. Il m’a toujours poussée à me dépasser et à donner le meilleur de moi-même. A mes yeux, il est devenu bien plus qu’un simple promoteur et je luis dois en grande partie d’être celle que je suis aujourd’hui. Je n’ai pas de plus grande fierté que celle d’avoir pu travailler durant six ans à ces côtés. Philippe, un merci ne suffirait pas!

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Contents

1 Introduction 17

1.1 Context and Motivations . . . 17

1.2 Objectives . . . 21

1.3 Organization of the Manuscript . . . 22

2 Baker’s Yeast Production 25 2.1 Introduction . . . 25

2.2 Saccharomyces cerevisiae: a Model Organism . . . 26

2.2.1 History . . . 27

2.2.2 Nutrition and Growth Conditions . . . 28

2.2.3 Main Metabolic Reactions . . . 31

2.2.3.1 Central Carbon Metabolism . . . 32

2.2.3.2 Central Nitrogen Metabolism . . . 36

2.2.3.3 Storage Carbohydrates Metabolism . . . 37

2.3 Industrial Production Process . . . 39

2.3.1 Baking Characteristics . . . 41

2.3.2 Medium Composition . . . 42

2.3.3 Bioreactor Description: Monitoring and Control . . . 44

2.3.4 Process Operating Conditions . . . 46

3 Modelling of Bioprocesses 49 3.1 Introduction . . . 49

3.2 Simulation and Modelling . . . 51

3.2.1 What Kind of Models? . . . 51

3.2.2 Macroscopic Modelling . . . 53

3.2.2.1 Reaction Scheme . . . 53

3.2.2.2 Kinetic Expression . . . 54

3.2.2.3 Mass Balance Equations . . . 56

3.3 Parameter Estimation . . . 59

3.3.1 Experimental Database . . . 59

3.3.2 Identification Criterion and Algorithm . . . 61

3.4 Validation of the Model . . . 64

3.4.1 Direct and Cross-validation Tests . . . 65

3.4.2 Uncertainty Analysis . . . 66

3.4.2.1 Parameter Uncertainty . . . 66

3.4.2.2 Predicted Model Output Uncertainty . . . . 69

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3.5 Model of Sonnleitner and K¨appeli . . . 72

4 Materials and Methods 77 4.1 Microorganism and Medium Composition . . . 77

4.2 Bioreactor Description . . . 77

4.3 Inoculum Development and Experimental Conditions . . . . 78

4.4 Analytical Methods . . . 80

5 Modelling the Link between N and C Source Uptakes 83 5.1 Introduction . . . 83

5.2 Model-based Design of the Experimental Database . . . 84

5.3 Modelling of Coordinated Uptake of N and C Sources . . . . 88

5.4 Parametric Estimation and Validation of the Model . . . 93

5.4.1 Uncertainty Analysis on Predicted Model Outputs . . 103

5.5 Conclusion . . . 106

6 Modelling the Oxygen Dynamics 107 6.1 Introduction . . . 107

6.2 Theoritical Framework . . . 108

6.3 General Procedure for Introduction of Oxygen into the Model 111 6.3.1 Step 1: Transfer Coefficient Estimation . . . 112

6.3.2 Step 2: Pseudo-stoichiometric Parameter Estimation 128 6.3.3 Step 3: Kinetic Parameters Estimation . . . 131

6.4 Conclusion . . . 138

7 Model Extensions: Intracellular Metabolite Production 139 7.1 Introduction . . . 139

7.2 Modelling Trehalose Production . . . 140

7.2.1 Identification with the First Set of Experiments . . . . 141

7.3 Modelling Glycogen Production . . . 143

7.3.1 Identification with the First Set of Experiments . . . . 143

7.4 Conclusion . . . 146

8 Off-line Process Optimization and Control Strategies 147 8.1 Introduction . . . 147

8.2 Dynamic Optimization Techniques . . . 148

8.3 Optimization Criteria and Procedure . . . 150

8.3.1 CVP Approach with Mesh Refinement . . . 151

8.3.2 Mathematical Analysis of Optimal Operation . . . 154

8.4 Comparison of the Two Approaches . . . 165

8.5 Conclusion . . . 176

9 General Conclusions and Perspectives 177 9.1 General Conclusions . . . 177

9.2 Suggestions for Future Research . . . 180

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Contents

Bibliography 183

Appendices 191

1 - General Kinetic Model of the Nitrogen Uptake Rate 193

2 - Influence of theβ Factor 201

3 - Recorded Data Associated to theP O2 Measurements 205 4 - Second Step of thepO2 Procedure 211 5 - Cross-validation of the Complete Model 213 6 - Influence of Mesh Refinement in the CVP Approach 223 7 - Influence of λValues on Optimization Results 225 8 - Optimal solutions including Trehalose and Glycogen 231

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List of Figures

2.1 Central Carbon Metabolism (Raven et al., 2007) . . . 35 2.2 Central Nitrogen Metabolism (ter Schure et al., 2000) . . . . 37 2.3 Schematic representation of a bioreactor . . . 46 3.1 Schematic representation of “overflow metabolism” . . . 74 5.1 Ethanol time profile imposed for the 4 experiments . . . 84 5.2 Culture medium feeding profile imposed for the 4 experiments 85 5.3 Sonnleitner & K¨appeli’s model and experimental measurements 86 5.4 Correlation matrix of the identified parameters (dimθ= 17) . 95 5.5 Correlation matrix of the identified parameters (dimθ= 15) . 97 5.6 Model simulation of the non-measured variableα-ketoglutarate 100 5.7 Direct validation of the model - Exp. 1-4 . . . 101 5.8 Leave-one-out cross-validation of the model - Exp. 1-4 . . . . 102 5.9 Local approach for uncertainty analysis - Exp. 1-4 . . . 104 5.10 Global approach for uncertainty analysis - Exp. 1-4 . . . 105 6.1 Schematic representation of “film theory gas transfer” . . . . 111 6.2 Recorded data associated topO2 measurements - Exp. 4 . . . 115 6.3 1st kLaestimation: direct validation of OTR reproduction . . 117 6.4 1st kLaestimates evolution over the time for each experiment 118 6.5 Data obtained after pre-treatement . . . 119 6.6 2ndkLaestimation: direct validation of OTR reproduction . 120 6.7 2ndkLaestimates evolution over the time for each experiment 121 6.8 Data obtained after a sampling ofpO2measurements . . . 122 6.9 3thkLaestimation: direct validation of OTR reproduction . . 123 6.10 3thkLaestimates evolution over time for each experiment . . 124 6.11 4thkLaestimation: direct validation of OTR reproduction . . 126 6.12 4thkLaestimates evolution over time for each experiment . . 127 6.13 Dissolved oxygen measurements reproduction . . . 130 6.14 Correlation matrix of the identified parameters (dimθ= 18) . 133 6.15 Direct validation of complete model - Exp. 1-4 . . . 135 6.16 Direct validation of complete model - Exp. 1bis-4bis . . . 136 7.1 Direct validation of trehalose model extension - Exp. 1-4 . . . 142 7.2 Cross-validation of trehalose model extension - Exp. 1-4 . . . 142 7.3 Direct validation of glycogen model extension - Exp. 1-4 . . . 145

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7.4 Cross-validation of glycogen model extension - Exp. 1-4 . . . 145

8.1 Comparison of 3 optimal results obtained with CVP approach 153 8.2 States and feeding of 76 S.-A. optimal solutions . . . 161

8.3 Distribution of the parameters of 76 S.-A. optimal solutions . 162 8.4 Influence ofEmin set for the definition oft2 onXmax . . . . 163

8.5 CVP and S.-A. optimal solutions comparison - State . . . 165

8.6 CVP and S.-A. optimal solutions comparison - Feeding . . . . 166

8.7 CVP solution and measurements comparison - 1st Exp. . . . 167

8.8 Identification results and measurements comparison - 1st Exp. 168 8.9 CVP and S.-A. comparison with sample volumes - State . . . 169

8.10 CVP and S.-A. comparison with sample volumes - Feeding . . 170

8.11 CVP solution and measurements comparison - 2nd Exp. . . . 171

8.12 Identification results and measurements comparison - 2nd Exp. 173 8.13 Global approach for uncertainty analysis - CVP solution . . . 174

9.1 Direct validation - Generalized nitrogen kinetic - Exp. 1-4 . . 197

9.2 Cross-validation - Generalized nitrogen kinetic - Exp. 1-4 . . 198

9.3 Comparison of 3 direct validations with differentβ values . . 203

9.4 Recorded data associated topO2 measurements - Exp. 1bis . 206 9.5 Recorded data associated topO2 measurements - Exp. 2bis . 206 9.6 Recorded data associated topO2 measurements - Exp. 3bis . 207 9.7 Recorded data associated topO2 measurements - Exp. 4bis . 207 9.8 Recorded data associated topO2 measurements - Exp. 1 . . . 208

9.9 Recorded data associated topO2 measurements - Exp. 2 . . . 208

9.10 Recorded data associated topO2 measurements - Exp. 3 . . . 209

9.11 Recorded data associated topO2 measurements - Exp. 4 . . . 209

9.12 Dissolved oxygen measurements reproduction . . . 212

9.13 First cross-validation of the model - Exp. 1-4 . . . 214

9.14 First cross-validation of the model - Exp. 1bis-4bis . . . 215

9.15 Second cross-validation of the model - Exp. 1-4 . . . 216

9.16 Second cross-validation of the model - Exp. 1bis-4bis . . . . 217

9.17 Third cross-validation of the model - Exp. 1-4 . . . 218

9.18 Third cross-validation of the model - Exp. 1bis-4bis . . . 219

9.19 Fourth cross-validation of the model - Exp. 1-4 . . . 220

9.20 Fourth cross-validation of the model - Exp. 1bis-4bis . . . . 221

9.21 States and feeding of 40 S.-A. optimal solutions . . . 226

9.22 Distribution of the parameters of 76 S.-A. optimal solutions . 227 9.23 Comparison of optimal solutions by fixingλG andλN . . . . 228 9.24 Optimal solutions for trehalose and glycogen - 1st experiment 231

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List of Figures 9.25 Optimal solutions for trehalose and glycogen - 2ndexperiment 231

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List of Tables

2.1 The elemental composition of baker’s yeast . . . 29

2.2 Defined medium for cultivation of baker’s yeast . . . 30

2.3 Medium composition for baker’s yeast production . . . 42

2.4 Typical molasses composition . . . 43

3.1 Parameter values of Sonnleitner and K¨appeli’s model . . . 75

5.1 Identification of the model (dimθ= 17) - Exp. 1-4 . . . 96

5.2 Identification of the model (dimθ= 15) - Exp. 1-4 . . . 98

5.3 Confidence intervals for identified parameter values - Exp. 1-4 99 6.1 1st parameter identification (dimθ= 5) -kLacorrelation . . . 117

6.2 2ndparameter identification (dimθ= 5) -kLacorrelation . . 120

6.3 3thparameter identification (dimθ= 5) -kLacorrelation . . 123

6.4 4thparameter identification (dimθ= 2) -kLacorrelation . . 125

6.5 Identification of yield coefficients (dimθ= 3) - 6 experiments 129 6.6 Identification of the model (dimθ= 18) - Exp. 1-4/1bis-4bis . 134 7.1 Identification of trehalose model extension (dimθ= 3) . . . . 141

7.2 Identification of glycogen model extension (dimθ= 3) . . . . 144

8.1 Optimization results - Multistart S.-A. . . 161

8.2 Optimization results with sample volumes - Multistart S.-A. 169 8.3 Identification of the model (dimθ= 15) - 2ndExp. . . 172

9.1 Identification of the generalized model (dimθ= 17) - Exp. 1-4 195 9.2 Identification of the generalized model (dimθ= 16) - Exp. 1-4 196 9.3 Comparison of kinetic expression of nitrogen uptake rate . . . 199

9.4 Influence of theβ factor on parameter identification results . 202 9.5 Identification of yield coefficients (dimθ= 3) - 6 experiments 212 9.6 Influence of the initial number of feeding partitions . . . 223

9.7 Influence the number of refinement iterations . . . 223

9.8 Optimization results (dimθ= 6) - Multistart S.-A. . . 226

9.9 Comparison of optimization results by fixingλG andλN . . . 228

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List of symbols

a “operating” parameter

A α-ketoglutarate concentration in cell [g gX−1] AIRF rate of the gas input flow (airflow) [slpm]

b “operating” parameter c “operating” parameter

ci concentration of dissolved gas i in equilibrium with its partial pressure in the gas [mol L−1]

COR correlation matrix d “operating” parameter D dilution rate [h−1]

E ethanol concentration in bioreactor [g L−1] Fi volumetric feeding rate of componentξi[L h−1] Fin volumetric feeding rate [L h−1]

Fout volumetric outlet rate [L h−1]

G glucose concentration in bioreactor [g L−1] Gin glucose concentration in feeding medium [g L−1] Gin molar gas inflow rate [mol h−1]

Gout molar gas outflow rate [mol h−1] GLY glycogen concentration in cell [g gX−1] Hi Henry coefficient [L P a mol−1]

J(θ) identification criterion

ki pseudo-stoichiometric coefficient [g g−1]

kLa transfer coefficient of oxygen from gas to liquid [h−1] Kξi saturation constant [g L−1]

KG Monod constant of glucose [g L−1]

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KO Monod constant of oxygen [g L−1] KE Monod constant of ethanol [g L−1] KN Monod constant of nitrogen [g L−1] KA Monod constant ofα-ketoglutarate [g L−1] Ki inhibition constant [g L−1]

KI ethanol inhibition constant [g L−1]

KIA α-ketoglutarate inhibition constant of glucose uptake rate [g L−1] KIA2 α-ketoglutarate inhibition constant of nitrogen uptake rate[g L−1] KI2 nitrogen inhibition constant of nitrogen uptake rate [g L−1] N inorganic nitrogen concentration in bioreactor [g L−1] Nin inorganic nitrogen concentration in feeding medium [g L−1] O dissolved oxygen concentration in bioreactor [g L−1] Osat saturated dissolved oxygen concentration [g L−1] Oin concentration of oxygen in the inlet gas [mol L−1] Oout concentration of oxygen in the outlet gas [mol L−1] OT R oxygen transfer rate [g L−1h−1]

OU R oxygen uptake rate [g L−1h−1] P total pressure of the gas [atm]

Pi partial pressure of the gasiin the gaseous atmosphere [atm]

Pk sets of indices of the components which inhibit the reactionk pO2 partial pressure of oxygen expressed in percent [%]

P RESS total pressure of the gas [atm]

Q “operating” parameter

Qi gaseous outflow rate of componentξi [L h−1] Qij positive-definite symmetric weighting matrix Qin airflow at the inlet of the bioreactor [L h−1] Qout airflow at the outlet of the bioreactor [L h−1]

Qin,i mass flow rate of the componentifrom the inlet gas to the liquid phase [g h−1]

Qout,i mass flow rate of the component i from the liquid phase to the outlet gas [g h−1]

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List of Tables

rki) specific rate of reactionkinvolving the componentsξi[g gX1h1] R ideal gas constant [L atm K−1mol−1]

Rk sets of indices of the components which activate the reactionk S covariance matrix

s(xi,θj) absolute parameter sensitivity S(xi,θj) relative parameter sensitivity S(x˜ i,θj) semi-relative parameter sensitivity

SSE sum of squared differences between model predicted outputs and experimental measurements

ST IRR stirrer speed (agitation) [rpm]

T temperature [K]

T RE trehalose concentration in cell [g gX1] V culture medium volume [L]

VG gas volume inside the bioreactor [L]

VL liquid volume inside the bioreactor [L]

xˆ estimated variable x “real” variable

˜

x error on the estimated variable X biomass concentration [g L−1]

yN,in gas phase molar fraction of nitrogen in the inflow yN,out gas phase molar fraction of nitrogen in the outflow yO,in gas phase molar fraction of oxygen in the inflow yO,out gas phase molar fraction of oxygen in the outflow

yij(θ) vector of the simulated variables at the ith time instant in the jthexperiment

ymes,ij vector of measurements at theithtime instant in thejthexper- iment

αk kinetic constant β kinetic constant

βl,k inhibition coefficient of componentl in reactionk [L g−1] βIA2 α-ketoglutarate inhibition constant for uptake rate of nitrogen

[L g−1]

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βI2 nitrogen inhibition constant for uptake rate of nitrogen [L g−1] γm,k activation coefficient of componentmin reactionk

γN nitrogen activation constant for uptake rate of nitrogen γA α-ketoglutarate activation constant for uptake rate of nitrogen ϕk rate of reactionk[g h−1]

ξin,i concentrations of componentiin the feeding [g L−1] θ vector of parameters

θˆ estimated value of parameterθ

σ2 variances of measurement errors

µmax,k maximal specific rate of reaction [g gX1h1] μOmax maximum specific respiration rate [g gX1h1] μGmax maximum specific uptake rate of glucose [g gX1h1] μN max maximum specific uptake rate of nitrogen [g gX1h1] λ strictly positive given number

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List of publications

Abstract

Macroscopic modelling of baker’s yeast production and intracellular trehalose accumulation in fed-batch cultures. 32th Benelux Meeting on Systems and Control, March 26-28, 2013, Houffalize, Belgium.

Proceeding

Macroscopic modelling of baker’s yeast production and intracellular trehalose accumulation in fed-batch cultures. 26thVH Yeast Conference, April 15-16, 2013, Berlin, Germany.

Co-author publication

Dewasme, L., Richelle, A., Dehottay, P., Georges, P., Remy, M., Bogaerts, Ph., and Vande Wouwer, A. (2010). Linear robust control of S. cerevisiae fed-batch cultures at different scales. Biochemical Engineering Journal, 53, 26-37.

First author publication

Richelle, A., Fickers, P., Bogaerts, Ph. (2013). Macroscopic modelling of baker’s yeast production in fed-batch cultures and its link with trehalose production. Computers & Chemical Engineering, 61, 220-233.

Richelle, A. and Bogaerts, Ph. (2014). Off-line optimization of baker’s yeast production process. Submitted in Chemical Engineering Science.

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1 Introduction

1.1 Context and Motivations

Human beings have always tried to improve their control over biological processes they use every day. In recent decades, the quality requirements placed on the agri-food products, combined with performance and produc- tivity pressures in an increasingly competitive industrial context, have led to an evolution in the way we control production processes on an industrial scale. Specifically, the traditional methods leave more place for controlled procedures: on-line measurements on the process, use of regulators to control variables (e.g. temperature, pH), etc. (Alford, 2006; Harms, 2002; Karakuzu et al., 2006; Komives and Parker, 2003; Sch¨ugerl, 2001).

Due to its central position in our daily lives, the food is subjected to strong economic, environmental and social pressures. In recent years, food inci- dents and scandals have even raised those pressures further. We observe from the consumer an increasing demand in a more sustainable food pro- duction, as well as an increased interest in being informed about the safety, the origin and the technological aspects of the processes involved in food pro- duction. Managers of the agri-food industry have to answer to this request for change towards sustainable development, weighting environmental and social considerations in a profit-oriented context. However, moving towards sustainable food production systems leads, in most of cases, in an increase in short term costs while long term revenues remain uncertain (Day, 2011;

Wognum et al., 2011).

It is therefore interesting to ask ourselves the following question: is it possible to improve the production process without affecting the final product price?

This question was the central question of this work. Indeed, this PhD thesis can be summarized in a precept, “do more and better with the same”. This essay will make the case for a policy of optimization: improvement of a process without changing its underlying principles. It requires a thorough understanding of the mechanisms involved in the studied process.

As an example of optimization, consider the human being and its diet. First let’s define the food elements required for optimal development (i.e. optimal growth and physical activity support). It is commonly accepted that the efficiency of use of the nutritional resources will differ following how the sys- tem is applied in the daily life. For instance, if someone eats his entire daily

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ration at lunchtime, he will squander most of the resources available to him since his body cannot absorb all the nutrients at once. “Natural optimiza- tion” tends to favor a distribution of energy supply over different meals in order to have energy throughout the day. The logic of process optimization through mathematical modelling is very similar. It is necessary to acquire a lot of knowledge about the systems that surround us in order to better formalize mathematically their operation, which allows us to objectively de- termine the optimal process.

Improvements in the modelling and interpretation of dynamic systems have thus become key contributions to the control and optimization of food pro- duction processes. These represent real scientific challenges due to the inher- ent variability of the complex biological systems that are involved in these processes. Devising scientific methods that can capture and interpret this variability to define the optimal approaches are key to future industrial advances (Alford, 2006; Day, 2011; Harms, 2002; Karakuzu et al., 2006;

Komives and Parker, 2003; Sch¨ugerl, 2001).

To date, most studies focus on optimizing yield (amount produced relative to the amount of what was necessary to produce) and productivity processes (yield per unit of time) (Alford, 2006; Hunag et al. 2012; Pomerleau, 1990;

Renard, 2006; Ringbom, 1996; Sch¨ugerl, 2001; Valentinotti, 2003). These are essential criteria to ensure the sustainability of an economic activity. How- ever, in the logic of sustainable development, it is also necessary to focus our thinking on quality (compliance with the specifications of what is pro- duced). The main challenge then falls within the definition of quality itself.

This definition will depend on the case study considered and the context.

However, the reflection exercise is based on the same initial hypothetical:

consider the possibilities of producing more with less impact by optimally using the available resources. It is interesting to note that to take this ap- proach is, in fact, to perform an optimization of the yield of a process (Day, 2011; Wognum et al., 2011).

The topic of this doctoral research is yeast production in bioreactors, an essential process in many food industries. Within the food industry, yeast cultures are widely used. These yeasts can either provide the desired product (e.g. baker’s yeast and brewer’s yeast) or are used for the synthesis of the final product (e.g. yeast extract used as flavor enhancers) (Leveau and Bouix, 1993; Najfpour, 2006; Waites, 2001; Wang, 2009).

In terms of supervision and control of yeast cultures processes, the food industry can benefit from the significant progress made in the biopharma- ceutical industry, where the reproducibility of methods and standards of quality have long been the priorities in the management of production. A key difference between these two sectors is the added value of the products:

very high in the case of drugs, much lower in the food industry products.

Performance and productivity criteria have always been crucial in the food

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1.1 Context and Motivations

context. However, the quality criteria (compliance with the specifications of the product) are also becoming increasingly important in this sector. It is therefore essential to develop yeast cultures processes which are optimal in the sense of the above criteria (Karakuzu et al., 2006; Komives and Parker, 2003; Najafpour, 2006; Pomerleau, 1990; Reyman, 1992; Ringbom et al., 1996; Sch¨ugerl, 2001).

It should be noted that the current industry practice of optimizing the pro- duction of baker’s yeast is often intended to determine a feeding profile in culture medium over the time, at the stage of the process development (R&D sector), on the basis of a trial and error method. This process is long, te- dious, expensive and usually leads to suboptimal solutions. The develop- ment of a mathematical model allows researchers to objectively determine the optimal operating conditions with respect to production criteria. How- ever, existing mathematical models of baker’s yeast production processes often do not take into account the inherent constraints linked to produc- tion on an industrial scale (medium composition, time of culture, available probes for measurements, etc.). Moreover, most of them focus only on car- bon metabolism without taking into account other essential nutrient sources for yeast growth, such as the nitrogen source (Enfors, 1990; Hanegraaf et al., 2000; Karakuzu et al., 2006; Lei et al. 2001; Pham et al., 1998; Pomerleau, 1990; Reyman, 1992; Rizzi, 1997; Sonnleitner and K¨appeli, 1986). Never- theless, a good management of the nitrogen source is crucial in this process.

Indeed, the manufacturers in the industrial sector vary the nitrogen sup- ply over the time in order to influence yeast physiology. More specifically, proper management of the carbon-nitrogen ratio in the feeding medium can be used to vary the ratio in intracellular carbohydrates and proteins: the two main factors governing the qualitative aspects of yeast as a finished product (Najafpour, 2006; Randez-Gil et al., 2013; Kristiansen, 1994).

Hence, we can see a growing need for mathematical models that allow an ad- equate optimization of baker’s yeast production in the food industry. Indeed, the existing solutions suffer from several limitations:

- Models developed to describe the dynamics of culture are mostly confined to the carbon sources, regardless of the other basic metabolic reactions that greatly influence what happens within the cells, such as nitrogen metabolism;

- Models taking into account more specific metabolism, such as nitrogen metabolism, are often too complex to be used for process optimization purposes;

- Models developed at the academic level often do not take into ac- count the constraints inherent in an industrial production, where needs and objectives are different;

- Optimization criteria are often limited to productivity and/or

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yield without taking into account constraints linked to quality control of the final products.

These limitations are, in part, due to many as-yet-unanswered questions regarding how to conduct the production process to ensure some qualitative properties of the produced baker’s yeast:

- How to define the quality of yeast as a finished product?

- What are the intracellular factors influencing the quality of yeast?

- Can we act on intracellular factors influencing the quality of yeast by using only the feeding time profiles in carbon and nitrogen sources?

Naturally, these questions are intertwined and the answers of the last two questions are completely dependent on the definition of “quality”.

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1.2 Objectives

1.2 Objectives

The overall objective of this thesis is the development of a macroscopic math- ematical model (extracellular components) describing the effects of an inor- ganic nitrogen source on the central carbon metabolism of Saccharomyces cerevisiae and allowing a model-based optimization of the fed-batch baker’s yeast production process.

This model will be developed so as to reproduce the dynamics of sub- strate consumption (carbon and nitrogen) and ethanol production related to baker’s yeast growth during its production on an industrial scale.

This model will be constructed on the basis of an experimental field defined so as to be representative of the industrial conditions of the baker’s yeast production process (e.g. culture time, composition and concentration in the culture medium). In addition, the choice of measurement signals and action variables on the process will be done by ensuring their availability on currently-used production devices to guarantee effective implementation of the model in an industrial context.

Indeed, the definition of the experimental condition will be inspired by the devices of the partner Puratos (world leader in bakery, pastry, and chocolate) and the yeast culture experiments will be performed on a pilot bioreactor (3BIO Department) similar to those found in industrial research and de- velopment laboratories, ensuring the validity of this research at both the academic and the industrial levels.

Moreover, model extensions will be considered in order to allow the study of the possibilities of controlling aspects related to the produced yeast quality (activity, stability, and the resistance to stress conditions such as drying) through good management of the provided substrates and the extracellular culture environment. As part of this work, the quality of the yeast as a final product will be evaluated on the basis of intracellular carbohydrate content (glycogen and trehalose). In doing so, the purpose of these model extensions will be to describe the dynamics associated with the production of these metabolites.

This model will allow the objective determination of the operating conditions (supply of nitrogen and carbon sources) in the sense of a production criterion (quantity of produced biomass). These optimal conditions will be applied experimentally in order to validate the proposed solutions.

To conclude, the goal of this work is to provide tools for food production that managers in this sector can use to meet the growing demands of tomorrow’s consumers in the framework of sustainable agro-industrial development.

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1.3 Organization of the Manuscript

To present all the results issued from the questions outlined previously, this paper consists of seven chapters, excluding introduction and conclusion. The first two chapters are devoted to the theoretical aspects underpinning this work, so as to provide the reader with good global understanding. Note that many theoretical aspects will not be reviewed in details in order to reduce the content of this manuscript. Indeed, this work is at the crossroads of very different theoretical disciplines (biochemistry, physiology, microbiology, mathematical modelling, and engineering science applied in industrial tech- nology). Hence, it would be impossible to make any kind of inventory of all theoretical knowledge used in this thesis. Thus, we will refer the reader to the relevant literature references to clarify any of the elements introduced in these two theoretical chapters .

Thus, Chapter 2 will strive to give the reader an overview of the biological aspects of baker’s yeast (Saccharomyces cerevisiae) and its production in an industrial context. Chapter 3 aims at listing the main principles of biopro- cess modelling. This chapter will focus on the development of models at the macroscopic scale. The parametric estimation techniques and model valida- tion aspects will be developed and presented. The model of Sonnleitner and K¨appeli (1986), one of the most-widely accepted models in the literature for Saccharomyces cerevisiaegrowth, will be presented at the end of the Chapter 3.

Once these theoretical aspects are presented, the rest of the manuscript will present the main results obtained in the framework of this doctoral work.

Chapters 5, 6 and 7 will mainly concern modelling topics. Chapter 5 presents the development of a macroscopic model introducing the effect of nitrogen on the baker’s yeast production process. This chapter will also present a simpli- fied model-based experimental design that ensures the information content of the experimental field on which the model will be developed. For the sake of simplicity, the model presented in Chapter 5 does not include the effect of oxygen. Hence, Chapter 6 will introduce a simplified procedure for the introduction of this effect into the model. Chapter 7 will present two exten- sions of the model presented in Chapter 5 to the production of intracellular metabolites (trehalose and glycogen). To conclude this manuscript, Chap- ter 8 aims at determining an optimal operation strategy and will present a comparison between two approaches (numerical and semi-analytical) for an open loop optimization.

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1.3 Organization of the Manuscript

The set of mathematical tools used to develop and validate the model were chosen for their ease of implementation and ease of use for users who are not expert in modelling theories. Indeed, this manuscript aims to give to the reader a glimpse of the whole procedure associated with the development of a model:

- the definition of modelling objectives;

- the gathering of information about the system;

- the harvest of informative experimental data;

- the development of the model itself;

- the validation of the developed model and the mathematical tools associated with it, and finally;

- the use of the developed model for optimization and/or control purposes.

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2 Baker’s Yeast Production

2.1 Introduction

Baker’s yeast is a typical low value high volume commercial product. Baker’s yeast, in its final form, is mostly delivered as a solid block with about 25-29%

dry weight, composed of living cellsSaccharomyces cerevisiae, or as a dried powder (dry yeast) with about 95% dry weight. It is used as a leavening agent to raise the dough in the baking process (manufacture of the bread) by conversion of sugars present in the dough (mainly maltose) in a mixture of ethanol and gas bubbles of carbon dioxide (Kristiansen, 1994; Randez-Gil et al., 2013; Waites et al., 2001).

Moreover, the use of yeasts results texture variations in dough (e.g. glu- tathione synthesized by yeast may influence the rheology of the dough1), im- proved nutritional factors (supplying vitamins, energy booster, and immune- system enhancement) and the development of flavors (by the modification of chemical composition of bread dough), which confer the qualitative prop- erties of the bread (Kristiansen, 1994; Randez-Gil et al., 2013; Waites et al., 2001).

The baker’s yeast is a package of enzymes, rather than just the total mass of a cell population, produced with defined activity (effectiveness of carbon dioxide production) and shelf life, also called stability (ability to maintain this activity over the time). The composition of these enzyme packages is the main factor influencing the qualitative properties of the produced bread.

This composition is subject to optimization by strain development and con- trol of the fermentation process, but the quality improvement of the bread is mainly achieved through the specific know-how of manufacturers. This know-how is mostly a well-guarded industry secret, which means that very little information on production specificics is available. Indeed, there is a lim- ited academic understanding of the physiological and genetic determinants of commercially important properties. Hence, the performance of current commercial yeast was mainly obtained by decades of experimental research without considering a potential systematic optimization of the factors that

1The thiol group of the glutathione is able to reduce the disulfide bonds of the gluten present in the dough. This reduction leads to a softening of the dough facilitating its shaping.

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influence the quality of yeast as a final product (Kristiansen, 1994; Leveau and Bouix, 1993; Randez-Gil et al., 2013; Waites et al., 2001).

The aim of this chapter is to put into its context the production of baker’s yeast. After a historical introduction, the metabolic aspects influencing the nutrition and growth ofSaccharomyces cerevisiae will be addressed. These theoretical aspects will enable the reader to understand the techniques used at the industrial scale: from the choice of the composition of the culture medium to the operating conditions implemented in the course of industrial production.

2.2 Saccharomyces cerevisiae: a Model Organism

The cell is the basic unit of all life forms. Organisms can be composed of a single cell (unicellular) while others are composed of numerous cells (multicellular) enabling cell specialization within the organism. The cells are the seat of the vital processes of metabolism and heredity. Cells are divided into two categories: prokaryotes (eubacteria and archeans) and eukaryotes, which have a more complex internal cell structure, such as those of fungi, protozoa, algae and other plants and animals. All eukaryotes cells are formed by a nucleus (control center of the cell) surrounded by cytoplasm (fluid matrix) which is bounded by a cell membrane primarily composed of lipids and proteins. They also contain nucleic acids (DNA and RNA), the vectors of genetic information, along with ribosomes (site of protein synthesis) (Waites et al., 2001; Raven et al. 2007).

Yeasts can be defined as unicellular fungi reproducing by budding or fission.

The Saccharomyces genus belongs to the subfamily Saccharomycetaceae, which are class Ascomycetes (the largest class of fungi). Yeasts are het- erotrophic (use of compounds, food that comes from other organisms) and are found in a wide range of natural habitats. Their growth is dependent on a series of interactions between cells and the surrounding environment. This ambient medium provides nutrients but also creates a more or less favorable environment for cell growth, depending on the availability of organic carbon, temperature, pH, the presence of water, etc. Unlike most fungi, which are obligate aerobes, many yeast are able to grow both in the presence and ab- sence of oxygen (facultative anaerobe) (Leveau and Bouix, 1993; Waites et al., 2001).

Not only are yeasts the first microorganisms observed under the microscope, they are also the first eukaryotes whose genome has been sequenced. Yeasts are model organisms for scientists because in addition to being unicellular eukaryotes (many mechanisms such as cell division and metabolism are very

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2.2 Saccharomyces cerevisiae: a Model Organism

similar to those of higher eukaryotes, including mammals), they possess qual- ities that allow them to grow, study and use them as easily as prokaryotic microorganisms (Leveau and Bouix, 1993; Raven et al., 2007; Waites et al., 2001).

2.2.1 History

Fermentation is a process widely used throughout the History. It seems that the microorganisms, such as yeast, were used from the Neolithic, during the settling of man, in a wide range of food manufacturing processes: production of bread, dairy products and alcoholic beverages (beer and wine). Indeed, civilizations present in Mesopotamia such as the Sumerians (3000 BC) and the Babylonians (2000 BC) were among the first to use yeast to make alcohol but also as a leavening agent in baking. The term “fermentation” derives from the Latin verbfervere whose etymological meaning is “to boil, be in turmoil” and was used to describe the action of yeast on cereal grain or fruit extracts. From a theoretical point of view, the fermentation is defined as the biochemical transformation of organic compounds, with the aid of enzymes, in cellular energy that can be used in the absence of oxygen. Nowadays, the yeast used for baking is Saccharomyces cerevisiae, more commonly named

“baker’s yeast” (Leveau and Bouix, 1993; Najafpour, 2006; Waites et al., 2001)

Although fermentation has been used for a long time, the scientific basis of this process was only understood less than 150 years ago. Indeed, it is only in the years 1866-1876, with the birth of industrial microbiology and the culmination of the work of Louis Pasteur (1822-1895), that the role of yeast in alcoholic fermentation was demonstrated. Pasteur showed that the fermentation of beer and wine was the result of microbial activity, rather than being a process of chemical catalysis. He also noted that certain organisms could spoil beer and wine. In doing so, he devised the process of preservation of alcoholic beverage by heat, a process called “pasteurization”

which was a major contribution to food preservation. Moreover, he also demonstrated the aerobic and anaerobic characteristics of fermentation. In fact, the early progresses of industrial fermentation processes were achieved thanks, in large part, to the work and publications of Pasteur such as“Etudes sur le vin” (1866) and “Etudes sur la bi`ere” (1876) (Leveau and Bouix, 1993;

Najafpour, 2006; Waites et al., 2001).

The development of pure cultures techniques by Emil Christian Hansen (1842-1909) at the Carlsberg Brewery in Denmark was among the other most important advances that followed in this area. This technique, car- ried out for the first time in 1883, was used to perform brewing with pure strain using a yeast isolated by Hansen, referred to as Carslberg Yeast No. 1 (Saccharomyces carlsbergensis). Note that various strains ofSaccharomyces

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exist and the main difference between the strains used for baking and those used for beer production is their capacity to metabolize specific patterns of medium components (Najafpour, 2006; Waites et al., 2001).

The“skimming method”was one of the first methods used for the commercial production of baking strains ofSaccharomyces cerevisiae. This procedure, similar to the fermentation process used for the brewing and distilling pro- cesses, used cereals-based media with yeast floating on top of the fermenter.

The produced yeast was skimmed off, washed, pressed and dried. During the First World War, Germany had to develop new techniques to produce glycerol in order to support explosives production in large scale. In this context, Carl Alexander Neuberg (1877-1956) showed that the glycerol was produced during alcoholic fermentation and identified that the addition of sodium bisulfate in the fermentation medium was favorable for glycerol pro- duction. Moreover, due to the shortage of cereal grains during the war, the yeast industry had to find alternate raw materials for the preparation of fermentation media. Consequently, due to these factors, Germany quickly developed the technology of industrial scale fermentation (production capac- ity of about 35 tons per day) using molasses, ammonia and ammonium salts instead of media derived from cereals (Najafpour, 2006; Waites et al., 2001).

2.2.2 Nutrition and Growth Conditions

Microbial growth can be defined as the multiplication of the cell number by division of a pre-existing cell. This cell division requires the biosynthe- sis of cellular components. In all living systems, adenosine-5’-triphosphate (ATP) is the primary energy source needed for the biosynthesis of cellular components. Indeed, cells use the ATP at their disposal to power cellular processes requiring energy such as growth, reproduction and maintenance of cellular activity. Obviously, this biosynthesis requires that cells are fed with substrates. These substrates, which can be organic or inorganic nutri- ents, are oxidized to supply the cell in ATP and constitutive macronutrients (chemo-heterotrophic organism). These macronutrients (carbon, hydrogen, oxygen, and nitrogen) along with phosphorus and sulphur, are the principal components of major cellular polymers: lipids, nucleic acids, polysaccharides and proteins (Table 2.1). Hence, living organisms need various nutrients to ensure that the elemental composition of their system can be maintained (Leveau and Bouix, 1993; Raven et al., 2007; Waites et al., 2001).

Yeasts have relatively simple nutritional requirements. They draw from their environment the substrates that they use as sources of carbon, oxygen, ni- trogen, etc. Therefore, to perform yeast cultures, it is necessary to ensure that these nutrient sources are present in sufficient quantity. Indeed, in a

“good” growth medium, carbon sources must be present at relatively high concentrations, often around 1020g/Lor greater, as they provide carbon

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2.2 Saccharomyces cerevisiae: a Model Organism

Table 2.1: The elemental composition of baker’s yeast (Kristiansen, 1994).

Element %(v/v)

Carbon 48

Oxygen 31

Nitrogen 8

Hydrogen 7

Potassium 2

Phoshorus 1.5 Magnesium 0.3

Calcium 0.2

Sulphur 0.2

Trace elements 0.18 Trace elements: Zn, Fe, Cu, Na, Mn, Mo

“skeletons” for biosynthesis. Various carbon sources can be used by yeast (e.g. maltose, sucrose, fructose, acetate, etc.) but the preferred substrate of most microorganisms is glucose (Kristiansen, 1994; Waites et al., 2001).

Nitrogen is a major component of proteins and nucleic acids; a concentration of 12g/Lin nitrogen source must be provided to fulfill these requirements.

A variety of organic nitrogen compounds, such as urea and various amino acids, may be used as nitrogen source. However, inorganic nitrogen sources, such as ammonium salts, are often preferred for their ease of assimilation.

Phosphorus, and more precisely inorganic phosphate, is the unit energy ex- change of the cell2. This essential element is usually supplied in the form of a pH buffer (inorganic phosphate ions, often noted Pi) at concentrations that should not normally exceed 100mg/L. Sulphur is required for the production of the sulphur-containing amino acids (cysteine and methionine) and some vitamins. It is often supplied as an inorganic sulphate or sulphide salt at a concentration of 2030mg/L. Other minor elements, including calcium, iron, potassium and magnesium, are required at levels of few milligrams per liter. The trace elements, primarily cobalt, copper, manganese, molybde- num, nickel, selenium and zinc are needed in only microgram quantities per liter. Often, the only other complex compounds or growth factor required are vitamins, e.g. biotin, pantothenic acid and thiamine. Hydrogen and oxy- gen can be obtained from water and organic compounds. A typical defined medium cultivation is presented in Table 2.2 (Kristiansen, 1994; Waites et al., 2001).

All of these nutrients must be transported into the cell from the environ-

2Inorganic phosphate is essential in energy transduction, e.g. adenosine triphosphate (ATP) and nicotinamide adenine dinucleotide phosphate (NADP). Indeed, cells store and release energy by using the phosphate bonds of these compounds by using reactions of phosphorylation / dephosphorylation (Raven et al., 2007).

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