DYNAMIC METABOLIC MODELING OF LIPID ACCUMULATION AND CITRIC ACID PRODUCTION BY YARROWIA LIPOLYTICA

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Batch mode cultures

This type of culture is large used in the industry to guarantee a pure culture (Dochain, 2003). Batch cultures are mainly used to evaluate the growth of microorganisms on different substrates. They have the advantage of being easy to perform and could produce large volumes of experimental data in short periods of time. However, the optimization of the production of specific metabolites is difficult to achieve due to the lack of control on the substrate feeding (Stephanopoulos et al., 1998). In the case of lipid accumulation by Yarrowia lipolytica, these cultures aimed at studying the microbial behavior on the given substrates (Papanikolaou and Aggelis, 2003b, 2002). Those cultures started with a known value of C/N ratio that tends to infinite as nitrogen is being depleted enhancing lipid accumulation. Lipid to biomass yield of 0.3 – 0.4 g.g-1 were obtained after 40 hours of culture, where lipids were further consumed as the carbon source was been depleted (Papanikolaou and Aggelis, 2002). The lack of C/N regulation makes difficult to achieve high productivity of lipid accumulation in batch cultures. In such conditions, lipid accumulation was followed by citric acid production (Papanikolaou et al., 2006). These findings highlight the need to manage both carbon and nitrogen flows to optimize lipid accumulation and reduce citric acid production, which cannot be achieved on batch mode.

Continuous cultures

Continuous cultures allow the characterization of steady states for the determination of specific rates under well-defined environmental conditions (Adamberg et al., 2015). Here, the dilution rate is kept constant in order to the study the response to disturbances of a stable state. The drawback of using this type of culture is the laborious operation as large amounts of fresh, sterile medium have to be prepared and it requires long periods of time for achieving the steady state (Kasemets et al., 2003). Moreover, continuous cultures are rarely used in industrial processes because they are sensitive to contaminations. With a particular interest on lipid accumulation, the optimal dilution rate (D) is intrinsically linked to the optimal C/N ratio. Ykema et al., (1986) studied different C/N ratios by the regulation of substrate concentration. This led to a fine tuning of growth rate proving that lower growth rates promote more extensive lipid accumulation.
Papanikolaou and Aggelis, (2002), regarded the impact of dilution rates when Yarrowia lipolytica was grown on glycerol. The results showed that storage lipids were favored at low dilution rates, where the highest value (0.4 g.g-1) was attained at D = 0.04 h-1. On the other hand, when dilution rate was fixed to 0.01 h-1, Rakicka et al., (2015) studied the effect of glycerol concentration, where lipid to biomass yield of 0.46 g.g-1 was obtained with 250 g.L-1 of glycerol.
Even if good results were obtained in continuous cultures, their scale up is more complicated due to the diverse conditions to take into account such as sterile conditions and product recovery, among others (Beopoulos et al., 2009a; Dochain, 2008). For this reason, Fed-batch cultures should be preferable aiming industrialization of the process.

D-stat cultures

The D-stat approach is very useful to study the impact of an environmental parameter on cell physiology at constant dilution rate D. The concept of the D-stat is simple: one environmental parameter (e.g. temperature, pH, or cultivation medium composition) is smoothly changed whilst D and other parameters are kept constant (Adamberg et al., 2015). This type of culture has been used for the study of: (i) the transition of metabolism from carbon to nitrogen limitation by smoothly decreasing the N/C ratio in Saccharomyces cerevisiae and Saccharomyces urvarum (Kasemets et al., 2003); (ii) the dependence on galactose/arginine ratio of lactic acid bacteria (Adamberg et al., 2006); and (iii) the overflow metabolism by acetate co-utilization with glucose on Escherichia coli (Valgepea et al., 2010).
Regarding lipid accumulation, the impact of the ratio C/N was evaluated to identify the metabolic shifts of Yarrowia lipolytica at constant dilution rate, pH = 5.5, and T = 28 °C (Ochoa-Estopier and Guillouet, 2014). In this case, the best N/C ratio in the cultivation medium for producing lipids without carbon loss into citric acid was identified between 0.021 and 0.085 molN.Cmol-1. Although the insights obtained from this culture mode, it is not suitable for lipid accumulation due to the low dilution rates.

Fed-batch cultures

This culture is the most common operation in industrial practice because it allows controlling substrate additions as well as the environmental conditions, and it facilitates physiological studies for a limited period of time (Beopoulos et al., 2009a; Stephanopoulos et al., 1998). In addition, this operating mode is more recommended when the recovery of the products is carried out at intervals (e.g. intracellular accumulation) (Dochain, 2008).
For lipid accumulation, it is desirable to have a precise control and monitoring of carbon and nitrogen flow rates since both induce activation-deactivation of the metabolic pathways (Papanikolaou and Aggelis, 2011b; Ykema et al., 1986). In addition, this type of culture allowed a well management of the N/C ratio to ensure a production of lipids without citric acid, which was shown by Ochoa-Estopier, (2012) for Yarrowia lipolytica on glucose. In fed-batch culture, if the nitrogen feeding is considered constant, and the carbon flow rate is varying, lipid accumulation can be generally seen as two metabolic phases (Beopoulos et al., 2009a; Papanikolaou and Aggelis, 2011b): (i) Growth phase, and (ii) lipid accumulation phase.
Phase (i) occurs when all nutrients are available in the medium, and carbon source (i.e. sugars) is consumed. Structural lipids are produced around 5-10% w/w (Papanikolaou and Aggelis, 2010). The biomass produced in this phase is called catalytic biomass (biomass which no contains accumulated lipids).
Phase (ii), is activated by a nutrient depletion, mostly nitrogen, and an excess on the carbon source. Under these excess conditions, the exceeding carbon is stored in lipid bodies mainly in the form of TAGs accumulated inside the cell (Beopoulos et al. 2011; Meng et al. 2009). Catalytic biomass can also increase due to the accumulation of non-lipid materials such as polysaccharides.

Metabolic Flux Analysis (MFA)

Metabolic Flux analysis was proposed to quantify the metabolic fluxes relying on a known metabolic network and the QSSA (Varma and Palsson, 1994; Wiechert, 2001). MFA analyze the topology of the metabolic network at steady state at which each reaction occurs (Zamboni, 2011).
In this context, a set of measured fluxes is used in combination with the knowledge of cell metabolism to determine the non-measured fluxes. Furthermore, it is possible to use constraints imposed by the measured fluxes to offset the indeterminacy of the system (Llaneras and Picó, 2008). The reaction rates r is thus partitioned into two subgroups (vectors) regarding the mes r ( 1 rmes n ) measured fluxes and the unmeasured fluxes u r ( 1 ru n ), which are linked to their respective stoichiometric matrices mes S ( mes rmes n  n ) and u S ( r ru n  n ). The solution of equation (II.6) is then reduced to compute the unmeasured fluxes u r . as, .  .  0 u u mes mes S r S r (II.7).
When the system is determined, a unique set of values for the unmeasured fluxes that satisfy (II.7) can be calculated as, u u mes mes r S .S .r *   (II.8).
where * u S is the Penrose pseudo-inverse of the stoichiometric matrix of unmeasured fluxes (Llaneras and Picó, 2008).
Some examples of this method comprise the study of: transient processes in animal cell cultures (Herwig and von Stockar, 2002); lactate production in mammalian cells (Crown et al., 2012); and the optimization of ethanol from xylose by Candida shehatae (Bideaux et al., 2016). Nevertheless, its limitations deal with the number of fluxes that should be provided to MFA for the determination of the unmeasured fluxes (Maertens and Vanrolleghem, 2010; Trinh et al., 2009).

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Flux Balance Analysis (FBA)

FBA is based on convex analysis under a constraint optimization problem. This approach was developed by (Varma and Palsson, 1994) based on linear optimization. FBA is one of the most widely used algorithms for analyzing metabolic systems, to dynamic modeling (Papin et al., 2004; Ruppin et al., 2010). The main assumption of FBA is that cell evolves to achieve an optimal metabolic objective. Some commonly used objective functions include: production of ATP, production of a desired by-product, or growth rate (Edwards et al., 2002; Maertens and Vanrolleghem, 2010).
FBA employs linear programming (LP) to solve the equation (II.6) (Orth et al., 2010). The uptake fluxes are required to be given as an input to a LP problem where the other of fluxes are calculated to maximize a prescribed objective function (e.g. biomass yield) (Provost 2006; Song et al. 2014). This flux distribution is then used to understand the metabolic capabilities of the system. In the case of maximizing biomass concentration, the LP problem can be represented as, where the solution is constrained between a lower and an upper bound, L b and U b , respectively.
Thermodynamic constraints (Beard et al., 2002) can be also applied to define limits on the range of values for individual fluxes in the network.
There are several important issues that arise when analyzing the optimal metabolic flux distribution. First, FBA relies on a priori knowledge (measured fluxes), but the knowledge on the regulatory mechanisms (e.g. regulation of enzymatic reactions) are still lacking (Maertens and Vanrolleghem, 2010). Second, the optimal solution may not always correspond to the real flux distribution because the solution is bounded to attain an specific objective (Llaneras and Picó, 2008). To overcome these hurdles, assumptions regarding cellular behavior based on the optimal solution must be made. Some of them assume that cells have evolved towards an optimal behavior, and that the objective function that has been mathematically imposed is consistent with the evolutionary objective (Feist and Palsson, 2010). However, the efficiency of the method highly depends on proper selection of the objective function, which is intended to represent the whole system (complete metabolism of a microorganism). This is not an easy task since each objective leads to different solutions. This was proven by Schuetz et al., (2007) studied the effect of changing objective functions by evaluating flux prediction with 11 linear and nonlinear objective functions in Escherichia coli with eight adjustable constraints. One of the most popular tool used to compute FBA is the COBRA toolbox implemented in MATLAB (Becker et al., 2007; Schellenberger et al., 2011). Nevertheless, the advantage of FBA is that it needs less data than MFA (Song et al., 2014a).
FBA has been used for the genome‐scale reconstruction of the metabolic networks. For example, Escherichia coli K‐12 (Feist et al., 2007); Pseudomonas putida (887 reactions) (Puchałka et al., 2008), which was also used for predicting the growth yield (i.e. biomass/substrate); and Yarrowia lipolytica metabolism (1143 reactions) (Pan and Hua, 2012), where the model was analyzed in silico for 24 different substrates. FBA has also been applied for strain improvement by metabolic engineering, for example Koffas and Stephanopoulos, (2005) achieved higher product yield and productivities of lysine production with strains of Corynebacterium glutamicum. In general, FBA applications are focused on metabolic engineering, construction and analysis of genome-scale metabolic models, and the refinement of the existing bio-chemical/metabolic networks. A detailed review on applications is revised by Raman and Chandra, (2009).

Elementary Modes analysis

Elementary Modes (EMs) are defined as non-decomposable pathways consisting on the minimum set of reactions under quasi steady-state assumption (Schuster et al., 2002). They can be seen as the set of successive reactions to transform substrates into products. Table II.3 could be considered as an example to clarify this concept. Here, the sets of reactions in Table II.3 (a) are schematized on Table II.3 (b-d), which take into account three different paths to obtain P1 from S1 and S2 (Table II.3 b), P1 from S1 (Table II.3 c), and/or P2 from S2 (Table II.3 d).

Macroscopic Bioreaction Model (MBM)

Macroscopic Bioreaction Model (MBM) is another approach that tries to represent the metabolism dynamically. It was proposed by (Provost et al., 2006), where metabolism is described by a set of key macroscopic bioreactions that directly connect the substrates to products. This approach was also based under the QSSA, contemplating a balanced consumption and production of intracellular metabolites.
Elementary Modes (EMs) are used to express the metabolism by macroscopic reactions. As mention is section II.2.3, the EMs are computed by convex analysis, in which a convex cone includes the complete set of non-negative solutions (Figure II.2). However, the reduction of the set of EMs is achieved by imposing specific uptake and production rates. This addition lowers the number of EMs telling which EMs or which macroscopic bioreactions are sufficient to be combined in the spite of building a model that explains the extracellular rates.

Lumped Hybrid Cybernetic Model (L-HCM)

Lumped Hybrid Cybernetic Model was introduced by Song and Ramkrishna, (2010). This modeling framework is an extension, of HCM in which all the equations presented in section II.3.3 hold. The difference with HCM and the essence of L-HCM relies in getting the L-EMs. To do so, the EMs are classified into different families according to their commonalities (e.g. substrates shared among EMs). In each family, EMs are subdivided into biomass producing group (including both biomass and ATP-producing modes); and ATP-only producing group (referred to as B- and A- groups, hereafter).
Flux distribution at EM family level can be described using the HCM framework by representing the flux vector r as follows, F F r  Z r (II.25).
where F r is the vector of F n fluxes through the lumped elementary modes and F Z is ( r F n  n ) L-EM matrix. In an equivalent form F r can be expressed as M r . The lumped HCM considers that the Jth column vector of the L-EM matrix F Z is given by the following lumping rule   F J J B J J A J Z w z w z , , ,  .  1 . (II.26).
where the parameter J w is determined such that the Growth rate dependent on ATP Requirement (GAR) is satisfied. B J z , and A J z , denote the weighted average of the EMs producing biomass (and both biomass and ATP) (Group B) and ATP (Group A), respectively in the Jth family, and are calculated as, j L JB nv J j L JB nv B J J B J A J z z z 2 2 , , , or   (II.27).
The lumping of EMs is also reflected in the computation of the return on investment (ROI) p (II.23), which is redefined within the Jth family as J J p  . Under this regard, L-HCM assumes that the non-regulated rates kin M J r , for each Jth family are proportional to a sub ROI (sROI) ( J kin M J r  , ), which is in turn given as the yields of vital products.     A J B J J Y Y , ,  (II.28).

Table of contents :

CHAPTER I. AN OVERVIEW TO LIPID ACCUMULATION
I. OLEAGINOUS MICROORGANISMS
II. A GLANCE TO LIPID METABOLISM
III. GENERAL ASPECTS OF LIPID ACCUMULATION BIOPROCESSES
IV. CONCLUSIONS
V. REFERENCES
CHAPTER II. MODELING AND PROCESS OPTIMIZATION
I. UNSTRUCTURED MODELING OF LIPID ACCUMULATION
II. MODELING METABOLISM
III. CONTROL OF BIOPROCESSES
IV. STATE ESTIMATION
V. CONCLUSIONS
VI. REFERENCES
CHAPTER III. RESULTS
I. INTRODUCTION
II. REDUCTION OF METABOLIC MODELS BY POLYGONS OPTIMIZATION METHOD APPLIED TO BIOETHANOL PRODUCTION WITH CO-SUBSTRATES
III. DYNAMIC METABOLIC MODELING OF LIPID ACCUMULATION AND CITRIC ACID PRODUCTION BY YARROWIA LIPOLYTICA
IV. MODELING AND OPTIMIZATION OF LIPID ACCUMULATION DURING FED-BARCH FERMENTATION BY YARROWIA LIPOLYTICA FROM GLUCOSE UNDER NITROGEN DEPLETION CONDITIONS
V. MULTI-OBJECTIVE PARTICLE SWARM OPTIMIZATION (MOPSO) OF LIPID ACCUMULATION IN FED-BATCH CULTURES
VI. SOFT-SENSORS FOR LIPID FERMENTATION VARIABLES BASED ON PSO SUPPORT VECTOR MACHINES (PSO-SVM)
VII. DISCUSSION AND CONCLUSIONS
VIII. REFERENCES
CHAPTER IV. CONCLUSIONS AND PERSPECTIVES
REFERENCES

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