Analysis of reaction kinetics during chemostat cultivation of Saccharomyces cerevisiae using a multiphase microreactor

Biochemical Engineering Journal 105 (2016) 220–229

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Biochemical Engineering Journal journal homepage: www.elsevier.com/locate/bej

Regular article

Analysis of reaction kinetics during chemostat cultivation of Saccharomyces cerevisiae using a multiphase microreactor Rainer Krull ∗ , Gena Peterat Institute of Biochemical Engineering, Technische Universität Braunschweig, Gaußstraße 17, 38106 Braunschweig, Germany

a r t i c l e

i n f o

Article history: Received 2 June 2015 Accepted 22 August 2015 Keywords: Chemostat Biokinetics Kinetic Parameters Microbioreactor Scale-Down Yeast

a b s t r a c t This paper presents the determination of reaction kinetic parameters and the kinetic analysis of a chemostat cultivation performed using a multiphase microreactor (mMR). Saccharomyces cerevisiae was cultivated aerobically in continuous chemostat mode using an mMR. Steady-state biomass, substrate and ethanol concentrations were determined at dilution rates between 0.14 ≤ D ≤ 0.42 h−1 with a glucose-feed concentration of 10 g L−1 . Modelling the aerobic chemostat culture was based on stationary balance equations. Maximal specific growth rate and Monod constant were determined using different linearization methods. The aerobic yeast metabolism was considered using two validity ranges of the model: (a) with purely oxidative metabolism in which glucose was converted into biomass or was used for maintenance metabolism, and no ethanol was generated; (b) with oxido-reductive metabolism employing an active Crabtree effect, in which ethanol was generated at the expense of biomass production. The different yield coefficients could be determined using the plots of the specific substrate consumption rate qS = f(D) and the specific product formation rate qP = f(D), respectively. Using this model, the reaction kinetic parameters were determined from the stationary concentrations of the biomass, glucose and ethanol that were determined during aerobic cultivation in the mMR. Finally, the kinetic parameters were compared with those reported in the literature that had been obtained using laboratory-scale reactors. © 2015 Published by Elsevier B.V.

1. Introduction Microbioreactors (MBRs) are promising tools that have been developed for screening applications using cell-culture systems. These devices are particularly beneficial for biotechnological, pharmaceutical and medical developments and process optimization, e.g., in pharmacokinetic studies, drug-delivery experiments or metabolic-flux analyses that involve the use of expensive or limited-supply agents. Due to their low production costs, their small working volumes, their flexibility and their potential for the performance of information-rich experiments under wellcontrolled experimental conditions, these devices are also suitable

Abbreviations: CDW, Cell dry weight; crab, Crabtree effect; conti, continuous mode; DI, deionized; in, inlet; hMBR, horizontal microbioreactor; HPLC, high performance liquid chromatography; max, maximal; L, liquid; MBR(s), microbioreactor(s); mMR, multiphase microreactor; P, product; PAA, poly(acrylic acid); PDADMAC, poly(diallyldimethylammonium chloride); PDMS, poly(dimethylsiloxane); PEM, polyelectrolyte multilayers; RI, refractive index; S, substrate; UV, ultraviolet; X, biomass; YMD, yeast extract, malt, glucose; YPD, yeast extract, peptone, glucose. ∗ Corresponding author. Fax: +49 531 391 7652. E-mail address: [email protected] (R. Krull). http://dx.doi.org/10.1016/j.bej.2015.08.013 1369-703X/© 2015 Published by Elsevier B.V.

tools for scale-up/scale-down cultivation studies and biocatalytic process experiments. Some of the most promising alternatives to standard cultivation techniques utilize MBRs operated in a continuous and parallelized mode under steady-state conditions. This process mode allows the variation of independent process parameters and provides reproducible, reliable experimental data over a long period, and thus is suitable for the analysis of significant reaction kinetics. In contrast to the conditions in macroscale reactors, the small dimensions of microsystems typically result in laminar fluid flow and a high surface-to-volume ratio. In the case of continuous operation, there are several examples of MBR applications. Zhang et al. [1] cultivated Escherichia coli in a 150-␮L microchemostat using flow rates of between 30 and 120 ␮L h−1 , which corresponded to dilution rates ranging from 0.2 to 0.8 h−1 . To investigate biological reaction kinetics using the stationary-process data obtained during cultivation in a chemostat, Edlich et al. [2] developed a passive aerated horizontal MBR (hMBR) system with a 10-␮L reaction chamber. The hydrophobic Saccharomyces cerevisiae DSM 2155 strain was used as the model organism. This hMBR had a glass bottom and a soft poly(dimethylsiloxane) (PDMS) lid. Park et al. [3] monitored a S. cerevisiae culture grown in the continuous mode for 140 h. An

R. Krull, G. Peterat / Biochemical Engineering Journal 105 (2016) 220–229

Nomenclature A b c D d dh DO KS mS OD qP qS rP rX R2 t U’ uG V V˙ W Y

Area (m2 ) Constant, ordinate intercept (−) Concentration (g L−1 ) Dilution rate (h−1 ) Depth (m) Hydraulic diameter (m) Dissolved oxygen concentration (g L−1 ) Monod constant (g L−1 ) Endogenous maintenance coefficient (gS gCDW −1 h−1 ) Optical density (−) Specific product formation rate (gP gCDW −1 h−1 ) Specific substrate consumption rate (gS gCDW −1 h−1 ) Volumetric product formation rate (gP L−1 h−1 ) Volumetric biomass formation rate (gCDW L−1 h−1 ) Coefficient of determination (−) Time (s) Perimeter (m) Superficial gas velocity (m s−1 ) Volume (m3 ) Volume flow (m3 s−1 ) Width (m) Yield coefficient (−)

Greek symbols ˛ Growth-associated product yield coefficient (≡ YP/X ) (gP gCDW −1 ) ˇ Growth-independent specific product-formation rate (gP gCDW −1 h−1 )  Specific growth rate (h−1 )

example of the fed-batch mode, in which glucose was released at different feed concentrations to cultures for up to 48 h, was investigated by Wilming et al. [4]. The multiphase microreactor (mMR) presented here can be applied as a vertical microbubble column for biotechnological screening using suspended cells [5]. The advantages of this mMR are the following: (a) enhanced submerged cultivation, (b) aeration via an additional gaseous phase in the form of the rising microbubbles and (c) circumvention of the risk of blockage due to the carbon dioxide produced by the microorganisms because the gas bubbles are released through buoyancy in the upper part of the reactor. This mMR has a reaction volume of 57 ␮L and consists of a microtechnologically fabricated PDMS chip, created using UV-depth and soft lithography techniques, which was covalently bonded to a glass bottom via surface activation using an air plasma [6]. The patterned PDMS chip included a micronozzle, which allowed the generation of bubbles with diameters of a few hundred micrometers at the bottom of the upright mMR. Investigation of the gassing rates showed that the overall gas holdup was less than 30% and that sufficient degassing occurred. The rising bubbles induced the circular convection of the liquid due to drag forces and thus enhanced mixing by reducing the diffusion distances and preventing cell sedimentation. Sensor elements, such as fiber optics and needle-type microsensors, which were integrated into the mMR enabled real-time online monitoring of the optical density (OD) and the dissolved oxygen (DO) level. In addition to the mixing effect of the active gassing process, this process provided a supplementary oxygen supply with a volumetric mass transfer coefficient of up to 0.14 s−1 , thus fulfilling an important criterion for scaling-up aerobic biological processes [5]. The aim of the present study was to validate the applicability of the mMR as a tool for screening reaction kinetics in chemostat

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cultures. Therefore, the Crabtree-positive model organism S. cerevisiae CCOS 538 (ATCC 32167, Culture Collection of Switzerland AG) was cultivated in continuous mode, and the OD and DO values were monitored online, while samples were taken for offline analysis of the glucose and ethanol concentrations via HPLC. Using the stationary concentrations of the biomass, glucose and ethanol, the reaction kinetic parameters were determined and were compared with the published results obtained using macroscale reactors.

2. The reaction kinetic model of continuous cultivation of Saccharomyces cerevisiae Under anaerobic conditions, a large fraction of the glucose substrate is catabolized to form ethanol and carbon dioxide, which pass into the medium [7–9]. The aerobic degradation of glucose is energetically more favorable for yeasts. Glucose is utilized to form new biomass, carbon dioxide and water under aerobic conditions [7,9]. If there is only a certain amount of glucose (cS < cS,crab ) and sufficient oxygen available, the substrate is efficiently utilized at a high biomass related yield coefficient YX/S . However, S. cerevisiae is also able to take up and degrade glucose in higher amounts per unit of time as it can metabolize via respiration. The amount of glucose that is not metabolized via respiration can be used to produce ethanol via glycolysis. Producing ethanol under aerobic conditions at glucose concentrations above a critical level of cS > cS,crab is referred to as the Crabtree effect [10,11]. Thus, the resulting YX/S is reduced [7]. The Crabtree effect occurs at low glucose concentrations (e.g., cS < 0.1 g L−1 [7,12]) and low specific glucose uptake rates (qS,crab = 0.62 gP gCDW −1 h−1 [13]). If the glucose uptake rate is below a critical value, S. cerevisiae can metabolize ethanol aerobically as a substrate in diauxic growth [7,9,13]. The sudden change in the metabolism of Crabtree-positive yeasts grown under aerobic, continuous cultivation conditions is one of the most studied physiological phenomena in microbiology [14], for which a clear and unambiguous explanation has not yet been provided [15–17]. Many different attempts to explain the basis of this phenomenon have been described in the literature (see, among others [7,12,14,18–25]). A simple, pictorial model describing the stationary states in the chemostat mode was provided by Sonnleitner and Käppelli [23], which included the idea of the so-called bottleneck due to a limited respiratory capacity, in which only a finite amount of glucose could be completely metabolized oxidatively, whereas the excess glucose would have to be utilized for ethanol production. However, the unstructured model did not account for the intracellular regulatory mechanisms and therefore could not describe the resultant dynamic effects. A different model was developed by Jones and Kompala [18]. Their cybernetic model was based on the hypothesis that an organism always attempts to maximize its growth rate. Instead of modeling individual enzymatic reactions, including those involved in cellular regulatory mechanisms, each metabolic pathway (fermentation of glucose and oxidation of glucose or ethanol) was controlled by a key enzyme and the optimal strategy for synthesis and activity was represented by cybernetic variables. In some models, the metabolic pathways were resolved in great detail [21,24], whereas other models accounted for other effects, such as the existence of multiple stable steady-states depending on the selected change in the dilution rate [24], the occurrence of oscillations in intracellular and extracellular quantities [18] and other dynamic effects, such as the responses to pulse experiments [19] or to different process modes [18,22]. Substrate-limited growth in a continuous culture is a process that allows the investigation of stationary kinetic process parameters. The reaction volume V was maintained at a constant level through equivalent incoming and outgoing flow rates V˙ . This

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cultivation mode is also known as a chemostat, because it is a stable, self-regulating system with stationary states. Cell growth is ensured by having a constant concentration of a growth-limiting (chemical) compound in the feed flow. The medium within the reactor was assumed to be ideally mixed; thus, no concentration gradients existed and the concentrations of the extracted volume corresponded to those within the reactor volume V. At a steady state, the accumulation terms (dci /dt) would be equal to zero and the mass balances of the concentration of biomass (cX ), glucose (cS ) and ethanol (cP ) would be calculated as follows [26]:

  dcX = 0 = D × cX,in − cX +  × cX , dt   dc S = 0 = D × CS,in − CS − dt



(1)

 − mS YX/S

 × CX −

rP , YP/S

(2)

  dcP = 0 = D × cP,in − cP + rP , dt

(3)

where the dilution rate D was the quotient of the volume flow V˙ and the reaction volume V, the index “in” indicated the concentrations of the feed flow, the coefficient mS assumed the endogenous maintenance metabolism of the cells, the yield coefficients YX/S and YP/S referred to the portions of the substrate that led directly to the formation of the biomass and products. The volumetric product formation rate rP was determined using the empirical model of Luedeking and Piret [27–30], as follows: rP =

dcp = ˛ × rX + ˇ × cX , dt

(4)

where rX (= ␮ · cX ) was the volumetric biomass formation rate. The coefficient ˛ was defined as the biomass growth specific product formation yield coefficient YP/X and the coefficient ˇ was the growth-independent, but biomass concentration-dependent product formation rate. ˛ and ˇ were obtained from the plot of the



qS =

D × CS,in − CS CX



␮ + mS YX/S

=





cX = D·

 cP =

D · (cS,in − cS )



1 YX/S

˛+

ˇ D

+



+ mS +

ˇ YP/S

,

(8)

× cX .

(9)

To account for the Crabtree effect and the associated change in the metabolism of the yeast cells, the equations describing the stationary biomass concentration [Eq. (8)] and the product concentration [Eq. (9)] were divided into two different regions: (a) In region I (0 < D < Dcrab ), the yeast cells would grow according to ␮ = D < Dcrab . The substrate would be effectively used via a purely oxidative metabolism and would be completely channeled into biomass formation and maintenance metabolism. No ethanol would be generated. The specific substrate consumption rate qS and the specific product formation rate qP with ␣ = ˇ = 0 regarding Eqs. (8) and (9) can be expressed as:



qS = qp =

D × cS,in − cS



cX

 + mS , YX/S

=

(10)

D × cP = 0. cX

(11)

Using Eq. (10), YX/S and mS can be determined from the slope and the ordinate intercept, respectively. (b) In region II (Dcrab < D < Dwashout ), the Crabtree effect would be active. The shift in metabolism during continuous cultivation would be obvious when the dilution rate reached the critical value of Dcrab [9,13,31–33]. Glucose would be converted oxido-reductively and ethanol would be generated at the expense of decreasing the biomass yield. Because ethanol is an end-product of energy metabolism, ethanol generation would be strictly coupled to the primary metabolic activity and therefore would be strictly growthassociated [28]. Thus, the growth-independent part of product formation in Eqs. (4) and (9) can be omitted (ˇ = 0). The specific substrate consumption rate qS and the specific product formation rate qP in region II can be, respectively expressed as: +



˛ × ( − Dcrab ) = × YP/S





oxidative growth and maintenance



a YP/S



1 YX/S

+



˛ YP/S

slope





+ mS −





˛ × Dcrab YP/S



(12)



ordinate intercept b1

oxido−reductive

specific product formation rate qP = rP cX −1 = f ( = D). Here the slope ␣ represented YP/X and the intercept (qP at  = D = 0) the growth-independent product frate ˇ. In most cases, the biomass feed concentration was cX,in = 0. The equation shown below thus follows Eq. (1): D = ␮.

(5)

Thus, at a steady-state, the specific growth rate  would correspond to the flow rate D. Using the Monod model, the specific growth rate would derive from the following equation:  = max ×

cS , KS + cS

D · KS , max − D

D × cP = (˛ × ( − Dcrab )) = cX

(7)

˛ × Dcrab

a

  ×  −   slope

(13)

ordinary intercept b2

The kinetic parameters of this model can then be determined from the plots of qS = f(D) and qP = f(D). Eq. (7) was used to calculate the stationary substrate concentrations cS . To model the stationary concentrations of the biomass cX and ethanol cP depending on the dilution rate D, Eqs. (12) and (13) were solved for each concentration, as follows:



cX = D×

(6)

where max was the maximal specific growth rate for a theoretically infinitely high substrate concentration and the Monod constant was KS . The self-adjusting steady-state concentrations cS, cX and cP were determined based on Eqs. (1) to (6) as a function of the dilution rate D: cS =

qp =

cP =



D × c S,in − cS 1 YX/S

+

˛ YP/S





+ mS −

˛ × (D − Dcrab ) × cX . D

˛×Dcrab YP/S

(14)

(15)

When D ≥ Dwashout , biomass would be washed out of the reactor system. The ethanol concentration would decrease as D → Dwashout and the glucose concentration would reach its input value cS,in at Dwashout : Dwashout = max ·

cS,in . KS + cS,in

(16)

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The maximal specific growth rate max would theoretically be achieved if the substrate concentration were infinitely large. Therefore, Dwashout < max . 3. Materials and methods 3.1. Design, fabrication and hydrophilization of the multiphase microreactor 3.1.1. Fabrication and hydrophilization The mMR consisted of two major components, a patterned PDMS chip and a glass substrate. The PDMS chip was created by replica molding using a negative master using UV-depth, high-aspect-ratio and soft lithography techniques. The patterned PDMS chip was then covalently bonded to the glass substrate via surface activation using air plasma. This process enabled the fabrication of several enclosed microdevices, which are inexpensive, biocompatible and optically transparent. Furthermore, PDMS material is gas permeable and therefore permits a passive supply of oxygen [34,35]. The process of fabricating this material was explained in detail in Demming et al. [6]. The mMR used in this study had a rectangular cross-section. The hydraulic diameter (dh ) of the mMR can be given by the following equation: dh =

4 × A , U

(17)

where A was the cross-sectional area and U was the perimeter of the wetted area of the reactor. The geometric dimensions are shown in Table 1. The slenderness ratio (H/dh -ratio) of the mMR was ≈17 and the surface-to-volume (S/V)-ratio was ≈4 mm−1 . To prevent cells or bubbles adhering to the unmodified PDMS surface, the hydrophilization procedure established by Schmolke et al. [36] was performed. This modification involved the layer-by-layer deposition of polyelectrolyte multilayers (PEM) (a combination of poly(diallyldimethylammonium chloride) (PDADMAC) and poly(acrylic acid) (PAA)) on the interior of the capped microreactor. The previously described type of coating [PDADMACterminated PEM-surfaces (6.5 double layers)] [5] was used in the present study. 3.1.2. Design The schematic design of the mMR is depicted in Fig. 1. The device consisted of a reaction chamber with two fluidic channels for the inlet and outlet of the gas and liquid phases, respectively. Alignment channels for the fiber optic device were constructed at both sides of the mMR. Clamp and stop structures guaranteed accurate positioning of the fiber optic device and biconvex lenses corrected the numerical aperture, resulting in parallel beams that illuminated the reactor [37]. Due to the optical path being 6.7 mm wide (the width of the reactor), a sensitive analysis of the OD during cultivation could be achieved [6]. The mMR was filled with liquid cultivation medium through the upper inlet, and complete discharge could be accomplished through the lower outlet. The gas phase was introduced through a single nozzle placed at the bottom of the reactor and the gas exited the device at the top. Some improvements in the design and configuration of the microreactor that was previously described [5] were made to produce the microreactor that was used in this study, as follows: because foam was generated while conducting cultivation experiments using increasingly higher cell densities, the headspace of the new mMR was increased. Sterile medium was fed into the mMR from the top, some distance from the liquid surface, to prevent overgrowing occurring in the freshly fed medium. Additionally, a PTFE tube (dO = 0.9 mm, di = 0.4 mm) that was freely movable was affixed over a piston seal near the top of the new mMR for efflu-

223

ent removal. Because the effluent was conveyed at a volume flow higher than that of the eluent, the reactor volume was maintained at a constant level. Varying the height of the effluent removal site allowed adjusting the reaction volume. Two fluidic channels were integrated in the upper and lower region of the reactor chamber to allow for surface modification using a flow-through process. The design of the fiber optic channels was also modified to allow technologically robust applications [38]. Sensor channels were also added to the new mMR at several positions, which allowed the optional integration of additional needle-type instruments, such as DO-fiber optic microsensors. If necessary, the thin PDMS membrane shielding the sensor channel from the reactor interior could be punctured. 3.1.3. Experimental setup The continuous cultivation experiments were performed using a custom-made incubation chamber (450 mm × 750 mm × 450 mm). The humidity was maintained at a constant level using an ultrasonic humidifier (230 V/50 Hz, Mercateo, München, Germany). The temperature was controlled using a system that included a Pt100-sensor element (connected to the mMR), a controller (KT4, Panasonic, Hamburg, Germany), a heater (LM 220-240 V/AC 57 W, RO/SE, Blechverarbeitung, Bad Birnbach, Germany) and a Peltier element (UEPK-S2AH-24 V-100 W, Uwe electronic, Unterhaching, Germany). Compressed air was filter-sterilized (Minisart, 16596 HY 0.2 ␮m; Sartorius Stedim Biotech, Göttingen, Germany) via regulation using a precision pressure valve (LRP-1/4-0.7, Festo, Hannover, Germany) and a metering valve (M3A-H0 L-V-SS-TC, DELTA-Fluid Industrietechnik, Braunschweig, Germany) that were connected to the gas inlet. Aeration of the mMR could be interrupted for OD measurements using an electrically switched three-port/two-way valve (24 V DC; Cetoni, Korbussen, Germany) while the flowing gas was released to the atmosphere. Using this configuration, aeration could be reapplied with minimal disturbance of the culture [5]. Precision glass syringes (5-mL SYR H-C 1/4 -28 UNF tubing connector, PTFE-seal; ILS Innovative Labor Systeme, Stützerbach, Germany) operated using a precision syringe pump (Nemesys, Cetoni, Korbussen, Germany) were used for liquid handling and the connection to the mMR was achieved using flexible Teflon tubing (PFA, dO = 1.59 mm, di = 0.75 mm; IDEX Health & Science, Techlab, Braunschweig, Germany) and cannulas (dO = 0.8 mm; Sterican, B. Braun, Melsungen, Germany), the latter of which were inserted into the fluidic channels and were glued to the mMR to prevent leakage. The liquids were conveyed via sterile feed lines using a degasser (VWR International, Darmstadt, Germany) within the precision syringe-pump system. For HPLC analysis of the glucose and ethanol concentrations, the effluent was passed into interchangeable refrigerated sample vessels (0.2-mL centrifuge tubes, Biozym Scientific, Hessisch Oldendorf, Germany). For rapid heat transfer, the sample vessels were cooled (Peltier element) in an aluminum block. The temperature selected caused the samples to freeze as soon as they contacted the wall of the sample vessels. 3.2. Strain, inoculum and cultivation medium The Crabtree-positive S. cerevisiae strain CCOS 538 (ATCC 32167), a culture of which was obtained from the Culture Collection of Switzerland AG, was used in this study because it has been described in numerous publications and investigated in numerous studies (e.g., see [13,23,39–48]) and is thus well suited to be a model organism. This strain has favorable hydrophilic properties, including no observable tendency to flotation and aggregation [44] and low adhesivity to the PDMS-reactor surfaces [49].

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Table 1 Geometric dimensions (width: w, depth: d), and hydraulic diameter (dh ), as defined using Eq. (17), of the reaction chamber and nozzle and the liquid-filled volume of the investigated multiphase microreactor (mMR). Reactor chamber (w × d) [␮m2 ] 6700 × 529.9

Nozzle dh [␮m] 982.1

Reactor volume

(w × d) [␮m2 ] 40 × 20

dh [␮m] 26.32

VL [␮L] 57

Fig. 1. Multiphase microreactor (mMR), including the reaction chamber, fluidic inlets and outlets, nozzle, adjustable-height effluent tube, fiber optic channels with alignment and clamp structures and biconvex cylindrical lenses for correcting the numerical aperture.

The cells of the obtained live culture were incubated (Certomat BS-1, Sartorius, Göttingen, Germany) in YMD medium (containing BactoTM yeast extract, BactoTM malt and ␣-D(+) glucose monohydrate, each at 20 per g L−1 ) at 30 ◦ C for 24 h in shaker flasks (3 baffles, filled to 20% [vol/vol] of the maximum level) with shaking at 120 revolutions min−1 . The cell suspension was then diluted using glycerol ≥ 99% (at a ratio of 2:3) and was stored as a cryo-culture at −80 ◦ C. The cells were reactivated by growing them on YPD-agar (20 g L−1 yeast extract, 10 g L−1 BactoTM peptone, 20 g L−1 glucose, and 20 g L−1 agar) culture media at 30 ◦ C for 3 d, after which they were stored at 4 ◦ C. A chemically defined cultivation medium, pH 4.5 (similar to that previously described [2,5]) was used [containing per liter: 3 g KH2 PO4 , 0.5 g MgSO4 ·7H2 O, 5 g (NH4 )2 SO4 , 0.1 L L−1 of 100 g L−1 Na-succinate (pH 4.5)] for all of the experiments. The stock solutions were autoclaved separately. For continuous cultivation, an aliquot containing 10 g of glucose, as well as 0.5 mL of a vitamin solution and 0.5 mL of a trace-element solution were added to each liter of medium as sterile solutions. The vitamin solution (pH 6.5) contained (in g L−1 ): 0.05 biotin, 1.0 Ca-d-pantothenate, 1.0 nicotinic acid, 25 myo-inositol, 1.0 thiamine hydrochloride, 1.0 pyridoxal hydrochloride, and 0.2 paminobenzoic acid. The trace-element solution (pH 4) contained (in g L−1 ): 16.6 Na2 EDTA·2H2 O, 4.5 ZnSO4 ·7H2 O, 1.57 MnCl2 ·4H2 O, 0.3CuSO4 ·5H2 O, 0.4 Na2 MoO4 ·2H2 O, 3.39CaCl2 , 3.0 FeSO4 ·7H2 O, and 0.1 KI. All of the chemicals were purchased from Merck (Darmstadt, Germany) or Sigma Aldrich (St. Louis, MO, USA). To prepare an inoculum for a main culture, the cells were grown in shaker flasks (Schott, Mainz, Germany, 20% [vol/vol] filled), at an initial OD value of 0.4 (SmartSpec 3000 spectrophotometer, Bio-Rad Laboratories, Munich, Germany) at 30 ◦ C overnight with shaking at 120 revolutions min−1 .

3.3. Determination of optical density and cell dry weight During the macroscale experiments, the OD values at 600 nm were determined offline using a spectrophotometer (SmartSpec 3000, Bio-Rad Laboratories, Munich, Germany), using deionized water (DI-H2 O) as the reference. The OD values were measured in duplicate; if necessary to bring the measured values within the linear range (0.1 ≤ OD ≤ 0.45), the samples were diluted using DI-H2 O. The concentration of cell dry weight (CDW) was determined gravimetrically using defined amounts of cell suspensions with known OD. The samples were collected from the shaken flasks during the glucose-based exponential-growth phase. Previously dried (108 ◦ C for 48 h, then cooled in a desiccator) and weighed (fine scale, LPA225D, Sartorius, Göttingen, Germany) filter units (RC-woven reinforced, Sartorius Göttingen, Germany) were used for cell separation. To remove the residues of the medium, the filter cakes were washed using the same volume of DI-H2 O as that of the medium, and then the filter units including the cells were dried (60 ◦ C for 52 h, then cooled in a desiccator) and weighed. The CDW concentration cX was then determined from the difference between the weights of the filter unit with and without cells and depending on the sample volume. For correlation purposes, in addition to determining the CDW and the OD of the culture in the mMR, the number of cells ncells in the cell suspensions was determined using a hemacytometer (Thoma new, depth: 0.100 mm, area: 0.0025 mm2 , Brand, Wertheim, Germany). Assuming a constant cell composition and thus unaffected absorbance characteristics, the OD measured in the mMR and using a spectrophotometer as well as the CDW concentration cX of a cell suspension could be correlated using the Lambert–Beer law. The following correlation equation was used (R2 = 0.960) to determine

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the biomass concentration cX during the continuous cultivation of S. cerevisiae in the mMR: cX

g

CDW

L

I 

= 2, 23135 · ln

0

I

mMR

− 1, 26528.

(18)

After at least four residence periods, a sample was collected for the offline analysis of the glucose and ethanol concentrations via HPLC. In addition, images of the aerated and non-aerated mMR were collected to detect possible changes in the reaction volume due to foaming. If this phenomenon was observed, the dilution rate was increased. 3.4. Offline analysis of the glucose and ethanol concentrations using HPLC A conventional isocratic HPLC system (LaChrom Elite, VWRHitachi, Darmstadt, Germany) equipped with an Aminex HPX-87H column (Bio-Rad Laboratories, Munich, Germany) was used to determine the glucose and ethanol concentrations. Cell-free samples were obtained by centrifugation (4 ◦ C, 13,000 revolutions min−1 , 4 min, 5415R, Eppendorf, Hamburg, Germany). Depending upon the volume of the sample, either a supernatant or a filtrate (centrifugal filter unit, 0.22 ␮m, Merck Millipore, Darmstadt, Germany) was prepared. A 20-␮L aliquot of each sample was injected into the HPLC system. H2 SO4 in the amount of 0.5 mM was used as the mobile phase, at a flow rate of 0.6 mL min−1 . After a retention time of approximately 9.8 min and approximately 22.7 min, the glucose and the ethanol peaks were detected using a refractive index (RI) detector. Calibration curves were generated by analyzing samples with known glucose or ethanol concentrations. 3.5. Cultivation procedure for the multiphase microreactor The mMR was introduced into the incubation chamber and all of the sensors and fluidic connections, except those for that for the gas supply, were connected. All of the connectors were sealed using silicone adhesive (RS Components, Corby, UK) to prevent leakage. For subsequent volume determination during the continuous cultivation of the cells, the mMR was filled in 5-␮L increments with a NaCl solution (0.9% wt.) and images were captured (using a digital microscopic camera, DigiMicro 2.0 scale, dnt, Dietzenbach, Germany) for each increment. Then, the entire system, including the air ducts and the channels requiring surface modification were purged using ethanol (70% vol.) until no air bubbles were visible. The outgoing connections were closed, and then an excess pressure was generated by slowly feeding ethanol into the mMR. After the flexible PDMS wall of the mMR was noticeably slightly curved, the feed flow was stopped. The pressure in the system was maintained for at least 20 min. Using this procedure, the entire mMR system was disinfected and checked for leakages and any residual air was eliminated from it. The outgoing connections of the system were then reopened, and the air supply was connected to the mMR using a sterile filter. The ethanol within the gas channel of the mMR was slowly replaced by adjusting the pressure at the nozzle. After drying a sterile filter, it was placed over the exhaust duct. Under sterile conditions, the NaCl solution was fed into the feed reservoir of the precision syringe pump system to fill it, and the mMR was carefully rinsed. For continuous operation, the cultivation medium was fed into the feed reservoir and the mMR and the liquid channels (inlet and outlet) were thoroughly rinsed. The effluent flow rate and the aeration rate were then adjusted. For conditioning and verifying the operation of the mMR and the peripheral-setup components (the incubation chamber and the sensors), the system was operated overnight while the inoculum was prepared, as described in subchapter 3.2. After the reference intensity for the OD-value calcu-

Fig. 2. Determined stationary concentrations of biomass cX , glucose cS and ethanol cP during the continuous cultivation of S. cerevisiae CCOS 538 in the mMR at different dilution rates D and a glucose-feed concentration of 10 g L−1 .

lations was recorded, the effluent was placed near the bottom and the mMR was emptied. The prepared inoculum was then passed through a syringe into a separate channel located immediately above the microfluidic system while the effluent was simultaneously removed. After flushing the inoculation line, the height of the effluent was adjusted to the desired mMR volume, after which the mMR was filled with the inoculum. At the beginning of the cultivation procedure, the aeration rate was readjusted and the interval switch and the systems for the OD intensity measurements at 600 nm and the DO measurements were activated. Initially, cell cultivation was conducted in a batch mode. At the end of the glucose-based, exponential growth phase (at approximately 7.5 h), the feed flow was adjusted according to the desired dilution rate and thus, the continuous cultivation period was initiated. The dilution rates were increased successively in the range of 0.14 ≤ D ≤ 0.42 h−1 during the continuous cultivation. The glucose concentration of the feed was set to achieve a final concentration of 10 g L−1 in the mMR. After at least three residence periods (at the respective dilution rate), the effluent was passed into a sampling vessel. 4. Results and discussion 4.1. Continuous cultivation To determine the values for the kinetic parameters, screening experiments were performed in the chemostat mode, as described in subchapter 2.5. A glucose feed concentration of cS = 10 g L−1 was provided and a liquid reaction volume of VL = 57 ␮L and a gassing rate of 2.23 L L−1 min−1 (corresponding to a superficial gas velocity of 5.9 · 10−4 m s−1 ) were set. Using these processing parameters, the measured DO concentration during aerated operation was greater than 84 %; thus, the oxygen supply was not limited. The values determined for the stationary cx , cS and cP depending on the dilution rate D are shown in Fig. 2. The stationary biomass concentrations were determined based on the recorded and averaged OD signal according to Eq. (18). The values represent the mean values and standard deviation calculated from analyzing samples collected after three and four theoretical volume changes (depending on the dilution rate D). The greatest concentration of biomass cX = 3.5 gCDW L−1 was achieved at a dilution rate of D = 0.12 h−1 . The corresponding yield coefficient was YX/S = 0.35 gCDW gS −1 . A distinct plateau of

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Table 2 Kinetic constants max and KS of the Monod model determined using the Lineweaver–Burk (Eq. (19)), Eadie–Hofstee (Eq. (20)) and Hanes–Woolf (Eq. (21)) linearization methods for continuous cultivation in the mMR and the published data of Rieger et al. [13] and von Meyenburg [32,33]. Lineweaver–Burk

mMR Rieger et al. [13]

von Meyenburg [32,33]

Eadie–Hofstee

Hanes–Woolf

cS,in [g L−1 ]

max [h−1 ]

KS [g L−1 ]

max [h−1 ]

KS [g L−1 ]

max [h−1 ]

KS [g L−1 ]

10 30 10 5 28

0.436 0.394 0.401 0.406 0.429

0.182 0.013 0.234 0.184 0.022

0.436 0.408 0.417 0.432 0.431

0.181 0.229 0.221 0.218 0.022

0.433 0.427 0.439 0.444 0.452

0.164 0.374 0.332 0.262 0.042

Table 3 Comparison of the kinetic constants YX/S , YP/S , ˛, mS and Dcrab of the model obtained using Eqs. (10)–(13) to describe the concentration profiles existing during continuous cultivation in the mMR and the published data of Rieger et al. [13] and von Meyenburg [32,33]; b1 and b2 are the intercepts of the linear regression line: b1 = −0.716 gS gCDW −1 h−1 ; b2 = −0.479 gP gCDW −1 h−1 .

mMR Rieger et al. [13] von Meyenburg [32,33]

cS,in [g L−1 ]

YX/S [gCDW gS −1 ]

YP/S [gP gS −1 ]

˛ [gP gCDW −1 ]

mS [gS gCDW −1 h−1 ]

Dcrab = (mS -b1 ) × YP/S /␣ [h−1 ]

Dcrab = −b2 /␣ [h−1 ]

10 30 10 5 28

0.335 0.473 0.471 0.481 0.502

0.715 0.683 0.559 0.505 0.500

2.637 10.117 7.548 7.834 5.445

– – – – 0.004

0.194 0.292 0.289 0.293 0.251

0.182 0.295 0.289 0.291 0.269

the biomass concentration achieved using only oxidative glucose metabolism at low dilution rates (region I) occurred at up to a value of approximately D = 0.19 h −1 . However, ethanol was detectable in the cultivation broth at a dilution rate of D = 0.16 h−1 . This phenomenon indicated the occurrence of an active Crabtree effect, which was corroborated by the general trend of a decrease in the biomass level while the ethanol level increased with increasing dilution rates and, furthermore, by the values determined for reaction kinetic parameters, as described below. Rieger et al. observed the onset of the Crabtree effect at a dilution rate of Dcrab = 0.3 h−1 [13], whereas von Meyenburg reported that Dcrab = 0.24 h−1 [33]. The different Dcrab values might have various explanations: during the cultivation process, the loss of cells in the overall medium due to sedimentation into the liquid channel (bottom left) was observed in the mMR, resulting in a lower biomass yield. Furthermore, the dilution rate steps might have been so abrupt that the resulting sharp changes in the glucose concentrations might have triggered the production of ethanol. Rieger et al. [13] showed that purely oxidative metabolism was not established until the dilution rates were decreased to within a range of 0.3–0.25 h−1 . Due to the conveyor principle of the mMR system, fluctuations in the level of the effluent were observed, with deviations of up to 5 ␮L, which resulted in a variation in the dilution rate in the corresponding interval. Furthermore, the composition of the medium affected the yield coefficients, and the occurrence of the shift in metabolism. For instance, not supplementing the medium with additives, such as yeast extract or amino acids [33], or limiting the supply of manganese [13] can reduce the Dcrab value. Another source of error might have arisen from determining the biomass concentration cX based on the measured OD value using Eq. (18). In this study, it was assumed that the optical property of the cell suspension did not change and that the dry weight per cell remained constant during continuous cultivation. However, von Meyenburg [33] reported a change in the dry weight per cell from 2.0 to 3.7 × 10−11 g cell−1 when the dilution rate changed from 0.035 to 0.38 h−1 . At the end of the chosen cultivation period, when higher dilution rates were used, wall growth was observed within the headspace of the mMR. Depending on the temporary, integral gas content, parts of the biomass were washed upward, distorting the OD signal. This phenomenon particularly affected the results of washout experiments.

The washout value Dwashout was experimentally determined through repeated rinsing of the biomass and was described using Eq. (16) as Dwashout = 0.425 h−1 . 4.2. Determination of the kinetic parameters The stationary concentrations of glucose (substrate), biomass and ethanol (product) during chemostat cultivation were mathematically described via Eqs. (7)–(9) and were dependent upon the dilution rate D. Then, the values for the kinetic parameters of the model were determined using different linearization methods, which are explained below in more detail. 4.2.1. Determination of the maximal specific growth rate max and the Monod constant KS Assuming the growth model of Monod [Eq. (6)], the maximal specific growth rate max and the Monod constant KS were determined using different linearization methods, including that of Lineweaver-Burk [Eq. (19)], Eadie-Hofstee [Eq. (20)], and HanesWoolf [Eq. (21)], respectively, as follows: Linearization according to Lineweaver-Burk 1 1 1 KS × + =  max cS max

(19)

Linearization according to Eadie-Hofstee  = −KS ·

 + max cS

(20)

Linearization according to Hanes-Woolf KS cS cS = +  max max

(21)

Graphical plots based on each of these linearization methods are shown in Fig. 3A (using the Lineweaver-Burk method), Fig. 3B (using the Eadie-Hofstee method) and Fig. 3C (using the Hanes–Woolf method). The values of the kinetic parameters were determined using linear regression. At a dilution rate of D ≥ 0.31 h−1 , the growth rate of the yeast cells depending upon the determined substrate concentration could be described with sufficient accuracy (R2 > 0.987) using these linearization methods. The validity of the Monod model at a glucose concentration of cS ≥ 0.09 g L−1 has been described by Dantigny

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227

Fig. 4. Stationary specific substrate consumption rate qS ( ) (eq. (12)) and specific product formation rate qP () (eq. (13)) while an active Crabtree effect was occurring at different dilution rates D during continuous cultivation in the mMR. The open data points were neglected in performing the linear regressions (lines). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

[18]. However, inaccuracies in the HPLC-based values may also justify neglecting glucose concentrations of cS < 0.013 g L−1 . The determined values for the kinetic constants max and KS are summarized in Table 2. For comparison, the values for the kinetic parameters that were determined in macroscale experimental studies of Rieger et al. [13] and von Meyenburg [32,33] are listed in this table. Comparing the values provided in Tab. 2 showed the dependence on the linearization methods. The max values calculated using the experimental data set deviated by up to 4% from the mean value. In the case of the macroscale cultivation experiments of Rieger et al. [13] that used a glucose feed concentration cS ,in of 30 g L−1 , the KS values deviated by as much as 72%, based on up to 33% deviation of the mean values of the given data set. The kinetic constants calculated for the mMR were therefore within the scattering range and were comparable to the values reported in the published studies [13,32,33].

Fig. 3. Determination of the kinetic constants max and KS of the Monod model using the linearization method of (A) Lineweaver–Burk (Eq. (19)), Eadie–Hofstee (Eq. (20)) and Hanes–Woolf (Eq. (21)) for the continuous cultivation of S. cerevisiae CCOS 538 in the mMR.

4.2.2. Identification of additional kinetic parameters Fig. 4 depicted the steady-state specific substrate consumption rate qS and the product formation rate qP as a function of the dilution rate D. As mentioned earlier in this chapter, ethanol was detected in the supernatant during continuous cultivation in the mMR at D = 0.16 h−1 . Therefore, no regression of the qS for purely oxidative metabolism in the mMR was determined using Eq. (10). Instead, the biomass yield coefficient YX/S was determined at a dilution rate of D = 0.12 h−1 using the difference ratio (cX /cS ) to yield YX/S = 0.35 gCDW gS −1 , whereas the maintenance metabolism coefficient mS was neglected. The values for the kinetic parameters for oxido-reductive metabolism were determined using linear regression, as shown in Fig. 4 (the open data points were neglected). These values are summarized in Table 3. Again, for comparison, this table includes the values for the constants that were determined by Rieger et al. [13] and von Meyenburg [32,33] using their data from macroscale experiments. The values determined for the stationary concentrations as a function of the dilution rate D are shown in Fig. 5. The dashed curve of the biomass concentration cX at low dilution rates (D → 0) was calculated using Eq. (14) using ˛ = 0, assuming an endogenous

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Fig. 5. Comparison of the values obtained using the reaction kinetic model, using estimations of the steady state glucose [cS , - - -; Eq. (7)], biomass [cX , —; Eq. (14)] and ethanol concentrations [cP , — —; Eq. (15)], and the experimental data (cS , ), ) for the continuous cultivation of S. cerevisiae in the mMR as a cx , 䊏) and (cP , function of the dilution rate D. The parameters used in the reaction kinetic model were: cS,in = 10 gS L−1 , 0.182 ≤ Dcrab ≤ 0.194 h−1 , (a)  = D < Dcrab (purely oxidative metabolism) max = 0.436 h−1 , KS = 0.182 gS L−1 , YX/S = 0.335 gCDW gS −1 , mS = 0 and cX , - - - with mS = 0.004 gS gCDW −1 h−1 , and ␣ ( YP/X ) = 0; and (b)  = D > Dcrab (oxidoreductive metabolism with an active Crabtree effect), the same values as above for max , KS and YX/S , YP/S = 0.715 gP gS −1 , ␣ (YP/X ) = 2.637 gP gCDW −1 , and mS = 0 [50]. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

maintenance metabolism coefficient of mS = 0.004 gS gCDW −1 h−1 , as determined from the experimental data of von Meyenburg [32,33]. The average deviation of the model values [obtained using Eqs. (7), (14) and (15)] and the measured values was in the range of 0 ≤ D ≤ 0.42 h−1 at approximately c = 0.22 g L-1 . Using the mathematical model, the onset of the Crabtree effect during cultivation in the mMR was found to occur when the dilution rate was in the range of 0.182 ≤ Dcrab ≤ 0.194 h−1 using a glucose feed concentration of 10 g L−1 . The difference in the Dcrab values determined using Eqs. (12) and (13) occurred because ethanol was detected at a dilution rate of D = 0.16 h−1 . In contrast, a significant reduction in the biomass concentration was found at D between 0.19 and 0.225 h−1 . Although the Dcrab values determined using the experimental and published data differed, a similar associated specific glucose uptake rate qS was estimated for the repression of oxidative metabolism. A value of qS ,crab = 0.537 ± 0.042 gS gCDW −1 h−1 was estimated for the mMR chemostat cultivation and an average qS ,crab = 0.616 ± 0.067 gS gCDW −1 h−1 was estimated using the data reported in the literature [13,32,33]. In comparison to the biomass yield coefficient found using the published data, which had values of between YX/S = 0.471 and 0.502 gCDW gS −1 [13,32,33], the value of YX/S = 0.335 gCDW gS −1 found using the mMR was low. As mentioned above, this phenomenon can be explained by the loss of cells in the lower liquid channel and by differences in the composition of the media. Furthermore, the wall growth in the headspace of the mMR at the end of the cultivation period and rinsing the biomass might also have distorted the steady-state values of the biomass concentration. These factors might be particularly likely to have caused an error at higher dilution rates and lower biomass concentrations. The resulting differences in the biomass concentration, which were also due to the previously mentioned inaccuracy of the ODcX -correlation in Eq. (18) directly affected the yield coefficients and were a possible cause of the deviations. The relatively low growthassociated yield coefficient of ˛ = 2.637 gP gCDW −1 determined in the mMR could also be explained by evaporation and the discharge of ethanol along with the exhausted gas.

The rate of fluid loss from the mMR was also examined at a relative humidity of 50% and 30 ◦ C. Aeration of glucose-free cultivation medium with an ethanol concentration of 5 g L−1 and a superficial gas velocity of uG = 5.9 × 10−4 m s−1 led to a fluid loss rate of up to 5 ␮L h−1 during the first two hours. In subsequent operations, condensation and back-flow of the medium in the head region that resulted in an evaporation rate of less than 0.6 ␮L h−1 was observed. This value was also confirmed for aeration of a 0.9% NaCl solution in the mMR system; in this case, an evaporation rate of 0.54 ␮L h−1 over a period of 25 h was determined [uG = 6.47 × 10−4 m s−1 and 2.4 L L−1 min−1 (vvm)]. At uG = 5.9 × 10−4 m s−1 , ethanol was stripped from the mMR at rates ranging from 0.23 to 0.39 gP L−1 h−1 [50]. Nevertheless, the general trend of a decrease in biomass and an increase in the ethanol concentration when the Crabtree effect was active was observed with an increasing dilution rate. With a further increase in the dilution rate to D → Dwashout , the wash-out of the biomass and ethanol as well as the increase in the glucose concentration occurred, as observed in Fig. 5. Although the compared reaction volumes, with values of 57 ␮L (mMR) and 2.5–2.85 L [13,32,33], were 50,000-fold different, the values for the kinetic parameters determined using the mMR were of the same order of magnitude or even within the same range as those of the kinetic constants determined using the published experimental data obtained at the macroscale. Moreover, the values determined in this study using continuous mode cultivation were consistent with those obtained when the model organism S. cerevisiae cultivated in the batch mode [5]. Both modes can be successfully implemented using the mMR system.

5. Conclusions In this study, the applicability of a multiphase microreactor (mMR) for aerobic submerged chemostat cultivation was investigated, and the resultant kinetic data were analyzed. The mMR used had a reaction volume of 57 ␮L and consisted of a microtechnologically structured PDMS-chip covalently bonded to a glass substrate and hydrophilized via a surface modification. The Crabtree-positive model organism S. cerevisiae CCOS 538 was used for chemostat cultivation. The values for the parameters of the reaction kinetic model were determined analytically using the experimental data for the stationary concentrations of biomass, substrate and ethanol on a microscale. The maximal specific growth rate max and the Monod constant KS were determined using linearization methods (Lineweaver-Burk, Eadie-Hofstee and Hanes-Woolf). Considering the empirical model of Luedeking and Piret, the yield coefficients YX/S , YP/S and ␣ ( YP/X ) were determined from plots of the specific substrate consumption rate qS = f(D) and the specific product formation rate qP = f(D), respectively. The kinetic reaction model was in good agreement with the experimental data and, hence, provided a good mathematical description of the biotechnological process. Considering the Crabtree effect on yeast metabolism, the two following validity ranges of the kinetic model were discussed in detail: (a)  = D < Dcrab , applied to purely oxidative metabolism, in which glucose was completely converted into biomass or was used for endogenous maintenance metabolism and no ethanol was generated, and (b)  = D > Dcrab , applied during oxido-reductive metabolism occurring under the Crabtree effect, in which ethanol was formed at the expense of biomass generation under aerobic conditions. The production of ethanol was strictly coupled to the metabolic activity occurring and was growth-associated. The data obtained using the mMR were then compared with the results obtained in chemostat experiments conducted on a macroscale in stirred tank reactors (2.5 and 2.85 L) by Rieger et al. [13] and von Meyenburg [32,33], respectively. Despite the volumes differing by

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