untitled CHEMICAL ENGINEERING TRANSACTIONS VOL. 27, 2012 A publication of The Italian Association of Chemical Engineering Online at: www.aidic.it/cet Guest Editors: Enrico Bardone, Alberto Brucato, Tajalli Keshavarz Copyright © 2012, AIDIC Servizi S.r.l., ISBN 978-88-95608-18-1; ISSN 1974-9791 Mathematical Modeling as a Tool to Describe and Optimize Heterologous Protein Production by Yeast Cells in Aerated Fed-Batch Reactor Lucia Paciello*a, Carmine Landia, Elisabetta de Alteriisb Palma Parascandolaa aDept of Industrial Engineering, Università degli Studi di Salerno, via Ponte Don Melillo, 84084 Fisciano, Salerno; bDept of Structural and Functional Biology, Università degli Studi di Napoli “Federico II”, via Cinthia, 80100 Napoli. lpaciello@unisa.it In this work, two recombinant yeast strains, the prototrophic non-conventional Zygosaccharomyces bailii [pZ3KlIL-1β] and the auxotrophic Saccharomyces cerevisiae BY4741[PIR4-IL1β], both producing human interleukin-1β, have been cultured in aerated fed-batch using glucose as limiting substrate. A mathematical model of the fed-batch reactor has been developed, based on mass balance equations of the main process variables -biomass, glucose and product- and implemented with kinetic expressions to explain the yeast behaviour within the aerated fed-batch reactor. In the case of Z. bailii, the mathematical model evidenced the suitability of the fermentative inoculum with respect to the respiratory one at the start of the exponential feeding. In the case of the auxotrophic S. cerevisiae BY4741, the modellistic approach has permitted to highlight a strong deviation from the expected behaviour and quantify the glucose amount that is spent for maintenance rather than for growth, thus impairing the outcome of the bioprocess. 1. Introduction The aerated fed-batch is the cultural system mainly employed in the production of recombinant proteins with glucose-sensitive yeasts (Mendoza-Vega et al., 1994; Porro et al., 2005). Indeed, fed-batch provides, through limited supply of one nutrient (generally the carbon and energy source), a suitable strategy to avoid over-flow metabolism, promote fully respiratory pathway and high yield of biomass and product of interest. Furthermore, fed-batch mode allows the proliferating biomass to be accumulated. This is a prerequisite to maximize volumetric productivity i.e. the amount of biomass and/or product in a given volume within a certain time, which is the most plausible target for optimization. Mathematical modeling of bioprocess is an useful tool to describe microbial cell growth, product formation and to optimize culture conditions. General attempts to model fed-batch processes have been described (Sinclair et al., 1987). Notwithstanding this, modeling of yeast high-cell density cultures and optimization of recombinant protein production need to be further developed, considering the peculiar environment represented by the aerated fed-batch reactor. In this concern, unstructured and non-segregated models, which describe the rate of growth based on the availability of a single substrate, may be easier and faster to develop and optimize with respect to the more sophisticated structured and segregated models. In this work, an unstructured non-segregated model has been developed to describe the fed-batch cultures of two glucose-sensitive yeast strains, the non-conventional prototrophic Zygosaccharomyces 79 bailii, and the auxotrophic Saccharomyces cerevisiae BY4741, both engineered for interleukin-1β (IL- 1β) production. In all the experiments, a medium properly formulated has been used, and the feeding strategy consisted in an exponentially increasing feed covering the entire run, which allowed the yeast strain to grow at a constant value of specific growth rate. The proposed unstructured and non- segregated model proved to be able of accurately describing and predicting key aspects of the fermentations, experimentally observed during yeast proliferation in the fed-batch reactor. 2. Materials and Methods 2.1 Strains The strain Z. bailii [pZ3KlIL-1β], kindly provided by prof. D. Porro, (UNIMIB-Italy), carried the plasmid pZ3KlIL-1β containing the human IL-1β gene expressed under the constitutive S. cerevisiae TPI promoter and, as selective marker, the resistance to geneticin (G418) (Vigentini et al., 2005). The S. cerevisiae BY4741[PIR4-IL1β] strain was obtained according to Paciello et al. (2010) by transformation of S. cerevisiae BY4741 (MATa,ura3Δ0, leu2Δ0, met15Δ0, his3Δ1) with the expression vector pIA1, containing URA3 as selectable marker and the human IL-1β gene functionally fused with a portion of PIR4 ORF. 2.2 Inocula preparation Strain samples, from the frozen cultures (-80 °C in 12.5% (v/v) glycerol), was grown at 30 °C in 500 ml flasks containing 100 ml of a defined mineral medium (Verduyn et al., 1992), pH 5.0. and 1% (w/v) casamino acids (BD Bacto™ Casamino Acids, BectonDickinson & Co., Sparks, MD 21152 USA) and made selective with 200 mg L-1 G418 in the case of Z. bailii [pZ3KlIL-1β]. Initial α-D glucose concentration was 5 and 2% w/v for Z. bailli and S. cerevisiae respectively. 2.3 Fed-batch cultures Fed-batch cultures have been performed at 30 °C in a 2.0 L working volume of a stirred fermenter, Bioflo 110 (New Brunswick Scientific). The fermenter initially contained 1 L of the defined mineral medium above mentioned. The fermenter was inoculated to give an initial O.D.590 of 0.04. As regards S. cerevisiae, fed-batch culture started after 15 h when glucose in the batch was exhausted, whereas for Z. bailli, fermentative and respiratory inocula were obtained with 18 and 30 h of batch phase, respectively. Then, an exponentially increasing feed was applied to allow the biomass to proliferate with a constant value of specific growth rate (0.13 h-1 and 0.16 h-1 for Z. bailii [pZ3KlIL-1β] and S. cerevisiae BY4741[PIR4-IL1β], respectively), lower than the 60% of the maximum specific growth rate of the strain (Enfors, 2001). The feeding solution contained glucose (50% w/v), salts, trace elements, glutamic acid, vitamins, and casamino acids, the concentration of which was calculated according to Paciello et al. (2010), taking into account the value of biomass yield for the given amino acid under aerobic conditions (Pronk, 2002). Oxygen was supplied by air sparging (DOT 30% air saturation).The culture pH was maintained at 5.0 by automatic addition of 2 N KOH during batch phase and 10% v/v NH4OH during exponential phase. The foam level in the fermenter was controlled by the automatic addition of the antifoam B (Sigma Aldrich) (dil. 1:10). 2.4 Determination of biomass, cell viability and specific death rate Total biomass was determined by optical density (O.D.590) and dry weight. The calibration curve relating O.D.590 values to biomass density provides a correlation factor of 2.0, and 2.45 O.D.590 per mg mL-1 for Z. bailii [pZ3KlIL-1β] and S. cerevisiae BY4741 [PIR4-IL1β], respectively. Viable cell density during fed-batch runs was determined by viable count (in triplicate) on YPD (1%Yeast Extract, 2% Peptone, 2% w/v Destrose) agar plates incubated at 30 °C for 48 h, and calculated according to: �(�) = �� ∙ ��� �� � ��� �� ��� (1) It was assumed that, at the start of feeding (t = 0), all the yeast cells were viable. The specific death rate (kd,) was evaluated as a first order kinetic constant by plotting the ratio CFU mL-1/ O.D.590 vs. time, where CFU corresponds to the colony forming units originated by viable cell count. 80 2.5 Analyses Samples withdrawn from fed-batch cultures were filtered on 0.45 μm GF/A Millipore filters and analyzed to determine residual glucose, ethanol and IL-1β concentrations in the culture medium (Paciello et al., 2010). All samples were analyzed in triplicate and the values of standard deviation obtained varied between 1 and 2%. 3. Mathematical model The unstructured non-segregated mathematical model was developed on the basis of component mass balances, starting from the differential equation written below which describes the change with time of the variable of interest (y, concentration, g L-1). �� �� = �(�) �(�) [�� − �(�)] ± �� · �(�) (2) qy is the specific rate of production or consumption referred to the generic variable y. The differential equation was numerically solved, by Eulero method, starting from given initial values. The first mass balance developed was that on the biomass x(g L-1): �� �� = − �(�) �(�) ∙ �(�) + �� · �(�) (3) The specific rate qx (h-1) includes the specific growth rate (μ, h-1) and the specific death rate (kd, h-1) (Tab.1). This equation was combined with the mass balance on glucose, the limiting substrate: �� �� = �(�) �(�) [�� − �(�)]− �� · �(�) (4) Glucose specific consumption rate (qs, h-1) is the overall specific rate of glucose consumption, including consumption for both growth (qg, h-1) and maintenance (qm, h-1). IL-1β production was modeled, considering that it is a growth-linked product : �� �� = − �(�) �(�) ∙ �(�) + �� · �(�) (5) where qp (h-1) is the IL-1β specific production rate. This latter is represented by the product between specific growth rate ( �) and product yield coefficient on biomass (�� �� ). Table.1: Kinetic expressions for fed-batch reactor with recombinant yeast strains Strain !" !# !$ Validity range Z. bailii [pZ3KlIL-1ββ] S. cerevisiae BY4741 [PIR4-IL1β] � � − %� � ∙ exp[−&(� − �')]-%� �( = ) *+ ,⁄ �( + � �( ∙ -��[−.(� − �')] + [/(� − �')0 + 1(� − �') + 2] � ∙ �� �� � ∙ �� �� {� ∙ exp[−&(� − �')]} ∙ �� �� ∀ t 0≤t. 0 10 20 30 40 0 4 8 12 16 20 0 4 8 12 R es id ua l g lu co se [g L -1 ] Bi om as s [g L -1 ] Time [h] A 0 1 2 3 4 5 0 30 60 90 120 0 10 20 30 IL -1 β [m g L-1 ] Bi om as s, r es id ua l gl uc os e [g L -1 ] Time [h] C 0 10 20 30 40 0 4 8 12 16 20 0 4 8 12 R es id ua l g lu co se [g L -1 ] Bi om as s [g L -1 ] Time [h] B 82 simulation curves and the experimental data regarding biomass and residual glucose (Figure 1A, B) highlighted that μ of Z. bailli [pZ3KlIL-1β] kept constant at the given value (0.13 h-1) only when the inoculum came from a fully fermentative batch culture (Figure 1A). During the fed-batch run carried out with the fermentative inoculum (Figure 1C), a good fitting between simulation curves and experimental data was observed. Glucose did not accumulate in the medium and ethanol was not produced (data not shown), indicating that Z. bailii [pZ3KlIL−1β] displayed a fully respiratory metabolism. A cell density of more than 100 g L-1 and a IL-1β concentration of 4 mg L-1 was achieved after 24 h, with a IL-1β productivity of 0.15 mg L-1 h-1. 4.2 Modeling of aerated fed-batch culture with S. cerevisiae BY4741[PIR4-IL1β] Differently from the bioprocess carried out with Z. bailii, the model for S. cerevisiae BY4741 (Table 1) considered that yeast cells did not remain viable over the entire fermentation run, since kd was significantly high (kd = 0.028 h-1). Figure 2 shows a good agreement existing between experimental data and simulation curves. It is evident that the specific growth rate (μ) chosen to build up the exponential feeding profile, was maintained in the time interval 0 ≤ t< t1 and exponentially decreased when t ≥ t.1 (see Table 1), where t1 corresponds to 7 h of feeding. Maximum of IL-1β productivity was achieved after 17 h (0.08 mg L-1 h-1) of feeding, then it diminished because cell density diminished, due Figure 2: S. cerevisiae BY4741[PIR4-IL1β] growing in the aerated fed-batch reactor: simulation curves (continuous lines) and experimental data refer to biomass (full rhombus),residual glucose (full triangle), and product (empty rhombus) concentrations.�� = 3.1 : ; <' , �� = 0 : ; <' , �� = 1.1 =: ;<' , �� �⁄ = 0.50, �� �� = 1 × 10