Introduction

Operational conditions determine the controlled environment experienced by mammalian cells when growing in suspension cultures, affecting process performance and product quality [1, 2]. Mixing aims to maintain cells suspended, promote a uniform distribution of temperature, pH, and nutrients, and ensure gas transfer (oxygen and carbon dioxide) [3, 4]. Conversely, mixing conditions produce hydrodynamic stress capable of potentially damaging mammalian cells [2, 5, 6]. Mixing and aeration in shake flask cultures are accomplished by controlling operational conditions such as the shaking frequency, the flasks nominal volume, the relative filling volume, and the shaking diameter [4, 7, 8]. Previously, it has been demonstrated that changes in those operational conditions can affect cell growth and viability, metabolism, and production in mammalian cells cultures associated with the inefficient gas transfer and the hydrodynamic stress generated [9,10,11,12,13].

In submerged cultures, oxygen transfer results from the aeration delivered at the gas–liquid interphase when flask cultures are shaken. Shaking leads to an increase in oxygen transfer by increasing the mass transfer area. Oxygen transfer rate (OTR) is mathematically defined by Eq. (1) in terms of the volumetric oxygen transfer coefficient (kLa) and the oxygen concentration gradient between the interfacial saturation and the liquid bulk (CL*–CL) [3, 14]. The kLa is an index of the oxygen supply efficiency, and it is proportional to the gas–liquid interfacial area (a).

$$\mathrm{OTR} = {k}_{L}a ({C}_{L}^{*} - {C}_{L}).$$
(1)

Due to the lack of cell wall and their larger size in comparison to microorganisms, animal cells are considered shear sensitive [3, 15,16,17,18], being one of the reasons for using low agitation rates (50–200 rpm) in cultures in shaken cylindrical containers [13, 19]. It has been shown that forces of different magnitude would promote cellular lysis or may induce other biological responses like reduced growth, cell death (apoptosis), or different metabolic reactions [5, 6]. Inside submerged cultures, two main fluid mechanical forces are present: shear stress associated with agitation and those related to gas–liquid interface due to sparging [2, 3, 20]. In non-baffled shake flasks, the first one must be considered since bubbles and foam generation are absent, and the flow regime is considered uniform [21,22,23]. Previously, it has been shown that hybridoma cell growth in shake flask is independent of the specific power input as a shear stress measurement [23]. However, not all animal cells are equally insensitive to a high agitation intensity [3, 11, 24]. The insensitivity of animal cells to hydrodynamic conditions was previously reviewed, covering TB/C3 mouse hybridomas, EBNA cells, HPV cells, and a CHO320 cell line, as well as insect cells [3, 20]. Recent work was published evaluating various orbitally shaken single-use cultivation systems (500 ml Erlenmeyer shake flask, the cylindrical TubeSpin bioreactor, and the alternately designed Optimum Growth flask) and presenting, as a result, a design space that allows optimal growth of a CHO cell line in submerged cultures [13]. However, the authors do not present lower volume shake flasks nor CHO cell lines producing recombinant proteins (RPs).

Here, we analyzed the culture performance of two recombinant CHO cell lines producing a humanized monoclonal antibody (mAb) with a 26-fold difference in their specific productivity (qP) [25] in terms of growth, cell viability, substrate consumption, metabolite, and ions accumulation and RP production, in suspension cell cultures growing in 250 ml Corning flasks shaken at different conditions (n = 60/120 rpm; d0 = 25.4/19.1 mm) and filling volume (10, 15 and 20%). These comparisons were made concerning the initial kLa, and volumetric power input (P/V) applied to submerged cultures.

Materials and methods

Cell lines and culture conditions

Cell lines CHO DP-12 clone #1933 CRL-12444 and clone#1934 CRL-12445 [26], which secrete a humanized anti-hIL8 monoclonal antibody (mAb), were acquired from the American Type Culture Collection (ATCC). Cells were cultured in CDM4CHO medium (Hyclone, Logan, UT, USA) supplemented with 6 mM stable glutamine (Alanyl-glutamine dipeptide, Biowest LLC, Kansas City, MO, USA), 0.002 mg/ml Humulin N (Eli Lilly, Indianapolis, IN, USA) and 200 nM methotrexate (Pfizer, New York, NY, USA), at 37 °C in a 5% CO2 atmosphere in a humidified incubator.

Cells from cultures with viability higher than 95% were seeded at 0.50 × 106 cells/ml in 250 ml Corning Erlenmeyer flasks (Cat. 431144, Corning, Glendale, AZ, USA), at 10 (25 ml), 15 (37.5 ml) and 20 (50 ml) % filled volumes, at 60 rpm (Cat. 7644-10115 Bellco Glass Inc., Vineland, N.J., USA, d0 = 25.4 mm) and 120 rpm (Thermolyne, Big Bill, USA, d0 = 19.1 mm). Cell concentration and viability were measured every 24 h by counting in a Neubauer chamber using the trypan blue dye exclusion method [27]. Culture time at which viability was above 90% was inferred from a 100 segments viability cubic spline curve generated by GraphPad Prism Software v5.01 (GraphPad Software, San Diego, CA, USA).

Quantification of metabolites, ions, and pH

The concentration of glucose, lactate, glutamine, glutamate, ammonium, sodium, potassium, and calcium in culture supernatants was measured every 24 h using BioProfile FLEX2 Automated Cell Culture Analyzer (Nova Biomedical, Waltham, MA, USA). Glucose concentration was also measured in the A15 automatized analyzer (Biosystems, Barcelona, Spain). Specific consumption or production rates were calculated during the exponential growth phase as the ratio between metabolite concentration and the integral viable cell concentration (IVCC), obtained as Area Under Curve using GraphPad Prism Software v5.01 (GraphPad Software, San Diego, CA, USA).

Quantification of specific productivity (q p)

Anti-hIL8 mAb concentration was measured every 24 h using Human IgG ELISA Quantitation Set (E80-104, Bethyl Laboratories, Inc., Montgomery, TX, USA), according to manufacturer´s protocol. SigmaFast OPD substrate (Sigma-Aldrich, Merck KGaA, Darmstadt, Germany) was prepared according to the manufacturer’s recommendations and incubated at room temperature for 15 min. The enzymatic reaction was stopped by adding 10% (v/v) HCl, and absorbance was recorded at 490 nm. qP values were calculated during the exponential growth phase as the ratio between product concentration and IVCC.

Volumetric mass transfer coefficient (k L a)

A 250 ml polycarbonate Corning Erlenmeyer flask was filled with 25, 37.5, or 50 ml of water and placed in an incubator with controlled conditions at 37 °C and 5% CO2 (NuAire, USA). Shaking frequency was set at 120 rpm with 19 mm shaking diameter (0.75 in) (Thermolyne, Big Bill, USA); or at 60 rpm with 25.4 mm (1 in) shaking diameter (Cat. 7644-10115 Bellco Glass Inc., Vineland, N.J., USA). The measurements of kLa were performed as described elsewhere [28] but subjected to the CO2 atmosphere. Briefly, measurements were obtained using the gassing-out method: oxygen was removed from water by adding Na2SO3 and CoCl2 as catalysts to achieve final concentrations below 6 × 10−3 and 5 × 10−7 mol L−1, respectively. Orbital shaker was started once oxygen-free water was assured, and the dissolved oxygen tension (DOT) was recorded online with an oxygen optical meter Fibox3 using a PSt3 sensor (PreSens, Regensburg, Germany). The sensor patch was attached at the bottom of the Corning flask, and the optic fiber was fixed in the shaker placed inside the CO2 incubator. The PSt3 sensors have a response time (measure at 63% of the response) near 14 s, which allows for the measurement of kLa up to 250 h−1 using the van’t Riet criterion [13, 29].

The kLa of four independent measurements per condition was obtained as the linear slope from a plot of the logarithmic expression against time Eq. (2) [5, 14, 27], where CL* = 100% saturated air, CL1 and CL2 are the DOT recorded at time points t1 and t2, respectively.

$$\mathrm{ln}\left(\frac{{C}_{L}^{*}-{C}_{L2}}{{C}_{L}^{*}-{C}_{L1}}\right)=-{k}_{L}a\times \left({t}_{2}-{t}_{1}\right)$$
(2)

For comparison purposes, kLa values were also calculated using the empirical correlation reported by Klöckner and Büchs [8] (Eq. 3).

$${k}_{L}a=0.0003212{d}^{1.92} {n}^{1.16}{ d}_{0}^{0.38} {V}^{-0.83},$$
(3)

where d is the maximum inner flask diameter (d = 0.08 m), n is the shaking frequency (s−1), d0 is the shaking diameter (m), and V is the filling volume (m3).

Calculation of power input (P/V), flow field and hydrodynamic parameters

P/V was calculated as a function of the operational conditions (Eq. 4) and the Reynolds number (Eq. 5) using the correlation proposed by Büchs et al. [21, 30], as follows:

$$\frac{P}{V}=\frac{C \rho {n}^{3}{d}^{4}}{{Re}^{0.2}{V}^{2/3}}$$
(4)
$$\mathrm{Re}=\frac{\mathrm{\rho n }{\mathrm{d}}^{2}}{\upmu } ,$$
(5)

where P/V is the power consumption per unit volume (W m−3), C is a non-linear fitting constant (C = 1.94), n is the shaking frequency (s−1), d is the maximum inner flask diameter (d = 0.08 m), and V is the liquid volume (m3). The physicochemical constants ρ (kg m−3) and v (Pa s) are the density and the dynamic viscosity of water at 37 °C since the cell/medium suspension is water-like [20].

Cell stress in the flow field inside shake flask cultures depends on cell size relative to an appropriate turbulent eddy length scale λ (m), measured by the Kolmogorov’s microscale of turbulence, which can be directly related to the energy dissipation rate (Ɛ) according to Eq. (6) [21, 23, 30, 31].

$$\lambda ={\left(\frac{\mu }{\rho }\right)}^{3/4}{{\varepsilon }_{0}}^{-1/4}.$$
(6)

The average energy dissipation rate Ɛ0 (W kg−1) for non-baffled flasks is obtained from Eqs. (7) and (8) in function of the Reynolds number (Eq. 5) [21, 30, 32].

$${\upvarepsilon }_{0}=\frac{\mathrm{Ne}\prime{ n}^{3} {d}^{4}}{{\mathrm{V}}^{2/3}}$$
(7)
$${\upvarepsilon }_{0}=\frac{\mathrm{Ne}\prime{ n}^{3} {d}^{4}}{{\mathrm{V}}^{2/3}}.$$
(8)

Ne′ is the modified power number for non-baffled flasks, influenced by the Reynolds number and the geometrical dimensions. Equation (8) resulted from the fitted model proposed by Büchs et al. [21, 30], for liquids with water-like viscosity and has a laminar (Re−1), a transition (Re−0.6), and a turbulent term (Re−0.2).

For calculation of the average shear stress τ (N m−2) and the shear rate γ (s−1), it is necessary to consider the average cell diameter dp (m), as indicated in Eqs. (9) and (10) [31].

$$\tau =0.0676{\left(\frac{{d}_{p}}{\lambda }\right)}^{2}{\left(\mathrm{\rho v }{\upvarepsilon }_{0}\right)}^{1/2}$$
(9)
$$\gamma =\frac{\tau }{v}.$$
(10)

Statistical analysis

All cultures were carried out three times. One-way ANOVA followed by Tukey’s Multiple Comparison Test was used when needed to estimate statistical significance in the culture parameters. Pearson correlation coefficient was determined for correlation analyses. A threshold significance level of 0.05 was applied for all analyses in GraphPad Prism v5.01. LOESS regression models were fitted to the experimental kinetic and stoichiometric parameters for CRL-12444 and CRL-12445 cells in R language to predict µ (α = 0.80), tD (α = 0.70), Xmax (α = 0.80), IVCC (α = 0.85), qP (α = 0.75), qGlc (α = 0.85), Lac/Glc ratio (α = 0.87) and qCa2+ (α = 0.80) values. Local polynomial regression fitting of second degree used experimental P/V and kLa as numerical predictors.

Results

The kLa values were measured at the different shaking rates and filling volumes chosen for culturing CHO cells (Fig. 1A). It has been previously shown that kLa increases with shaking frequency, flask size, and shaking diameter [4, 7, 8]. Our results show how by maintaining the same flask diameter, the shaking frequency of 120 rpm promotes higher kLa values compared with 60 rpm, even when the shaking diameter was lower (19.1 vs. 25.4 mm), which can be explained by the higher P/V values delivered at 120 rpm (Fig. 1B). A positive correlation between P/V and kLa experimental values was found in our study, explaining why P/V-derived results might mirror those from kLa (Pearson r = 0.94), although there is a sudden change between the two incubators used indeed due to the rotational diameter (19.1 vs. 25.4 mm; Fig. 1B). We can also observe that kLa is greater at the lower filling volumes (Table 1) as it is expected due to the higher interfacial area–volume ratio [28]. Figure 1A also shows the theoretical values of kLa at the different operational conditions according to an empirical model found in the literature (Eq. 3) [8], which were higher than the experimental values. Figure 1C shows the linear correlation between P/V, the average energy dissipation rate (Ɛ0), the average shear stress (τ), and the shear rate (γ), as Table 1 resumes. Thus, when analyzing the effect of P/V on recombinant CHO cells cultures, similar conclusions can be obtained with these hydrodynamic factors (Ɛ0, τ, and γ). However, there is a non-linear inverse correlation between P/V and the size of the turbulent eddy length scale measured by Kolmogorov’s microscale of turbulence (λ) (Fig. 1C). This Kolmogorov’s microscale of turbulence is considered an index of the potential cell damage. Whenever the cellular size is minor than λ, the hydrodynamic stress is not assumed as harmful [3, 20, 24, 31]. The typical cellular size of CHO cells is between 15 and 18 μm [33], so according to Kolmogorov’s theory, λ values estimated here between 45.4 and 80.9 μm (Table 1) are unlikely to cause cellular damage [20].

Fig. 1
figure 1

A kLa values of 250 ml Corning flasks shaken at 120 (fill dots) and 60 rpm (empty dots) maintained at 37 °C, 5% CO2, and varying the relative filling volume at 10, 15, and 20%. Means and standard deviations of four independent measurements are shown. Theoretical kLa values were calculated according to the model published by Klöckner and Büchs (2012) and are represented as a dotted line (120 rpm, d0 = 19 mm) and a straight line (60 rpm, d0 = 25.4 mm). B Relationship between volumetric power (P/V) and kLa for the 250 ml Corning flasks shaken at 120 (dots) and 60 rpm (triangles) at three filling volumes. C Relationship of P/V, the turbulent eddy length scale measured by the Kolmogorov’s microscale of turbulence (λ), the energy dissipation rate (Ɛ), the average shear stress (τ) and the shear rate (γ) as published in Table 1

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Table 1 Operational conditions used with the measured volumetric oxygen transfer coefficient, volumetric power input, flow field, and hydrodynamic parameters estimated for each experimental shaking condition of the 250 ml shake Corning flasks cell suspended cultures
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Thus, once the culture system was characterized in mass transfer and hydrodynamic stress, the effects of agitation rate and filling volume of the shake flasks on growth kinetics of two CHO cell populations secreting a humanized anti-hIL8 mAb were assessed (Fig. 2). The clone CRL-12444 remains viable (> 90%) at least 3 days more than clone CRL-12445. In addition, the cultures carried at 60 rpm present up to 10–45% more maximum cell concentration (Xmax) than those grown at 120 rpm (in almost all filling volumes evaluated). Sublethal effects could explain this due to elevated oxygen transfer rate or shear stress [34]. Kinetics of glucose, lactate, glutamine, glutamate, and ammonium concentration, and pH in supernatants in supernatants of CHO cell cultures are shown in Fig. S1. It is worth noting that the cultures carried at 120 rpm present up to 20.0–80.6% more glutamine in the supernatant than those grown at 60 rpm (in all filling volumes evaluated) when using the clone CRL-12444. Still, when using the clone CRL-12445, these differences in glutamine production were found only on the second day of culture (Fig. S1). Whether these glutamine concentrations reflect its specific consumption rate could not be known, because the biochemistry analyzer cannot quantify this amino acid as a dipeptide form. As has been reported in other cell lines, low oxygen conditions can promote glutamine uptake by increasing glutamine transporters, switching the fate of glutamine from the oxidative pathway into the reductive carboxylation pathway [35]. Moreover, kinetic of sodium, potassium, and calcium concentrations on culture media are shown in Fig. S2, and when comparing 60–120 rpm, no significant differences were found. However, both cell lines tend to consume more calcium at 120 rpm than at 60 rpm in flasks with 20% filled volume (Fig. S2).

Fig. 2
figure 2

Effects of agitation speed on growth kinetics of Chinese hamster ovary cells producing a monoclonal antibody. CRL-12444 (A–C) and CRL-12445 (D–F) cells were seeded at 0.5 × 106 cells/ml in 250 ml Erlenmeyer flasks at 10 (A, D), 15 (B, E) and 20% (C, F) filled volumes, at 60 (closed symbols) and 120 (open symbols) rpm. Viable cell concentration (circles in continuous lines) and viability (squares in dotted lines) of cultures were determined over time by the trypan blue dye exclusion method in a Neubauer chamber. Error bars represent the standard deviation of three biological replicates

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Kinetic and stoichiometric parameters were calculated for each experimental shaking condition of the suspension cultures in Corning flasks (Table S1) and plotted against the kLa (Fig. 3). The clone CRL-12444 statistically presented a higher maximum cell concentration at lower values of kLa (that corresponds to 60 rpm, d0 = 25.4 mm, Fig. 3). In contrast, a statistical significance for Xmax was only reached between 9.57 and 11.00 h−1 in the case of CRL-12445 cells. The rest of the parameters measured in CRL-1244 cells did not change in any condition (Fig. 3). In the case of CRL-12445, a higher qp was obtained at the mid-value of kLa (11.0 h−1, Fig. 3L), but without effect on the final concentration of the mAb (Fig. 3F). This is surely associated with the reduction in the IVCC in the same value of kLa (Fig. 3E). For these higher producer cells (CRL-12445) in this mid kLa value, it was recorded an increased glucose consumption (qGlc) (Fig. 3G) without changes in lactate production (qLac) (Fig. 3H), which translated into a lower Lac/Glc ratio (Fig. 3I).

Fig. 3
figure 3

Effects of kLa on kinetic and stoichiometric parameters of CRL-12444 (closed dots) and CRL-12445 (open dots) CHO cells producing a monoclonal antibody. Specific growth rate (µ, A), doubling time (td, B), maximum cell concentration (Xmax, C), time at which viability was above 90% (D), integral of viable cell density (IVCC, E), monoclonal antibody concentration (F) are presented. Moreover, specific consumption of glucose (G), specific production of lactate (H), glutamate (J), ammonium (K), and monoclonal antibody (L) were presented, as well as the ratio of glucose and lactate specific rates (I). Error bars represent the standard deviation of three biological replicates

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Comparing the kinetic and stoichiometric parameters based on P/V, the clone CRL-12444 statistically presented a higher Xmax at lower values of P/V (that corresponds to 60 rpm, d0 = 25.4 mm, Fig. 4). Like kLa, CRL-12445 presented a qp at the mid-value of P/V (66.6 W m−3, Fig. 4L) without effect on the final concentration of the mAb (Fig. 4F). It is worth noting that in both clones, the final concentration of the mAb was not affected as an effect of kLa or P/V (Figs. 3F, 4F). Though without statistical significance, a tendency to a higher growth rate and shorter doubling time was observed in both cell lines at lower kLa and P/V values. The same kinetic and stoichiometric parameters were plotted as a function of the filling volume and shaking rates in both clones in Fig. S3.

Fig. 4
figure 4

Effects of volumetric power input (P/V) on kinetic and stoichiometric parameters of CRL-12444 (closed dots) and CRL-12445 (open dots) CHO cells producing a monoclonal antibody. Specific growth rate (µ, A), doubling time (td, B), maximum cell concentration (Xmax, C), time at which viability was above 90% (D), integral of viable cell density (IVCC, E), monoclonal antibody concentration (F) are presented. Moreover, specific consumption of glucose (G), specific production of lactate (H), glutamate (J), ammonium (K), and monoclonal antibody (L) were presented, as well as the ratio of glucose and lactate specific rates (I). Error bars represent the standard deviation of three biological replicates

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Trends in µ, tD and calcium consumption for CRL-12444 cells, and the statistical differences in Xmax, IVCC, qP, qGlc, and Lac/Glc ratio for CRL-12445 cells were fully reflected on the predicted behavior of these parameters in correspondence with kLa and P/V values by regression models (Fig. 5).

Fig. 5
figure 5

LOESS regression models of kinetic and stoichiometric parameters of Chinese hamster ovary cells producing an anti-hIL8 monoclonal antibody under different P/V and kLa conditions. A polynomial surface of the second degree was fitted to experimental data using P/V and kLa as numerical predictors for µ (A), tD (B), Xmax (C), and IVCC (D) from CRL-12444 cells, and qP (E), qGlc (F), Lac/Glc ratio (G), and qCa2+ (H) from CRL-12445. The predicted z-axis ranges from high (red) to low (blue) values

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Discussion

Mammalian cells have a slow growth related to a low oxygen uptake rate compared to yeast or bacterial cultures [2, 3]. The kLa coefficient is not an index of cellular oxygen consumption, but it can be indirectly related. It has been reported that low values of OTR around 0.5–8 × 10–10 mmol L−1 h−1 are enough to supply the oxygen demand of a 107 cells ml−1 culture [36, 37]. Particularly, for CHO cells in suspension cultures, kLa typical values are usually in the range of 1 to 60 h−1 (Fig. 6, Table S2). For example, kLa values between 3 and 50 h−1 should satisfy oxygen demand for a 107 cells ml−1 culture [20, 37]. Here, we measured kLa values in water between 1.9 and 23.8 h−1 (Fig. 1A, B, Table 1), so it is expected that flasks shaken at 60 rpm, even the higher shaking diameter (25.4 mm), and the higher filling volumes are potentially more likely to promote oxygen restricted cultures, even more so when high cell densities are reached [13, 38]. Measured values of kLa at the different operational conditions were lower compared with the empirical model found in the literature (Eq. 3) [8]. As expected, theoretical values tend to be higher than the experimental kLa values since the Corning flasks are made of hydrophobic polycarbonate material. In contrast, the model presented was experimentally validated for hydrophilic glass flasks. Flask walls nature plays an essential role in oxygen transfer. It has been shown a film formation of liquid at flask walls that significantly increases gas–liquid interfacial area associated with the centrifugal movement of the fluid during the orbital shaking. The formation of this thin film is abolished in flask walls of hydrophobic nature [7, 39].

Fig. 6
figure 6

Relation of P/V and kLa values of CHO cell cultures obtained from the literature. Data were taken from Table S2. Stirred tank bioreactors (STR, circles); Orbitally shaken reactors (OSR, squares); Ambr™ systems (triangles); microplates (inverted triangles) and shake flasks in this work (filled diamonds)

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Furthermore, the oxygen transfer experimented by CHO cells is expected to be even lower due to solutes in culture media that negatively affects oxygen solubility (CL) and the global oxygen transfer coefficient (kL) [40, 41]. Moreover, since the controlled atmosphere inside the incubator has lower oxygen partial pressure than air, due to the CO2 atmosphere, the oxygen available is expected to be lower than that reported at similar conditions with orbitally shaken flasks [42]. Low oxygen transfer rates, related to lower agitation rates, could lead to variations of the culture pH [3, 42]. Also, CO2 produced could not be completely stripped out of the media, promoting physiologically dangerous levels of pCO2 [3, 42]. Even with all these problems, in our case, the production of a mAb being the main objective, we do not see important effects of the filling volume, diameter, and stirring speed, all associated with kLa, on the product titer (Fig. 3). Though final product titer and quality are two of the most critical parameters for a successful bioprocess, the changes in qP and metabolism experimented with by cells over time could give crucial clues for process improvement. In this line, intermediate kLa (11 h−1) and P/V (66.62 W m−3) values impact on productivity and metabolism of the higher producer cells (CRL-12445). The positive correlation between kLa and P/V values in shake flasks and most orbitally shaken single-use bioreactors derives from the impossibility of separating these variables. It is reflected in previous reports even in different culture conditions (Pearson coefficient r = 0.62, Fig. 6). CRL12445 cells at these mid values increase glucose consumption without changing lactate production, resulting in a lower Lac/Glc ratio. This higher efficiency in glucose conversion could contribute to the higher qP exhibited by CHO cells [43]. Thus, these intermediate ranges of kLa and P/V could be harnessed during bioprocesses to shift CHO cells toward a more efficient carbon metabolism and circumvent in this way the genetic engineering [44] or the challenging task of maintaining low nutrient levels [45] required for this purpose.

The volumetric power input (equivalent to the mean specific energy input rate) is dissipated in the bioreactor or shake flask through a series of eddy cascades, which eventually converts all mechanical energy into heat. Energy dissipation is the driving force for mixing and the cause of the hydrodynamic stress on the cells [16, 17]. Since mammalian cells have low oxygen demand, the rate of energy input is also low, typically between 1 and 10 W m−3, allowing efficient operation in shake flasks [2, 3]. Using the correlation proposed by Büchs et al. [21, 29] (Eq. 4), we estimated the power input values in function of the shaking operational conditions (Fig. 1, Table 1). Results obtained are between 9.6 and 15.2 W m−3 (n = 60 rpm) and 66.6–105.7 W m−3 (n = 120 rpm), which exceed the mean power input requirements for mammalian cell suspension cultures. Moreover, the values calculated agree with those previously reported [21, 30]. Compared with the kLa values measured for the Corning flasks, the hydrophobic nature of the flask walls has no relevant impact on the power consumption [21, 30].

To determine how significant the mixing shear stress is, we also calculated the turbulent eddy length scale (λ), the average energy dissipation rate (Ɛ0), the average shear stress (τ) and the shear rate (γ) (Eqs. 6–10). Those models for the hydrodynamic parameters are based on the turbulent regime flow (Re > 60,000). However, this condition is not fulfilled [32], but there is an advantage that the ratio of maximum and average energy dissipation rates is almost 1.0 [32]. Therefore, results in Table 1 corresponding to the hydrodynamic parameters for shaken flasks are only presented as an approximation and must be carefully interpreted.

At 120 rpm, the average energy dissipation rate (Ɛ0) calculated were 0.071–0.113 (W kg−1), while the average shear stress and the shear rate were 1.37–2.17 mN m−2 and 1.77–2.81 s−1, respectively (Table 1), considering an average cell diameter of 15 μm [33]. Those hydrodynamic parameters had low values and were even lower when calculated at the shaking frequency of 60 rpm (Fig. 1C, Table 1). Animal cells are insensitive to low shear stress, and no effects are reported associated with energy dissipation rates (Ɛ) lower than 100 W kg−1 [6, 17]. Animal cells death associated with high shear stress occurs typically with Ɛ values between 107 and 108 W kg−1. However, lethal effects have also been reported at Ɛ values near 103 W kg−1 [6, 17]. This literature information may help to explain why we do not find significant differences in mAb final concentration, besides some sub-lethal effects as a higher specific growth rate, a shorter doubling time, and a higher maximum cell concentration were found at lower values of P/V (mainly in the clone CRL-12444, Fig. 4). A few studies have published sub-lethal effects elicited by hydrodynamic forces, like slow growth, altered glucose metabolism, reduced productivity, and RP glycosylation profile change produced by CHO cells [15, 17, 46]; at Ɛ values between 103 and 105 W kg−1, which correspond to shear stresses on the order of 1–10 N m−2 [6, 17]. Moreover, no effect on cell viability or antibody-produced quality was found in three CHO cell lines cultivated in bioreactors with Ɛ values of 0.01–0.02 and 1 W kg−1 [3, 20].

Conclusions

Here, we show that hydrodynamic conditions inside non-baffled shake flasks are unlikely to elicit cellular damage with the previous data. Though these responses are line-specific, there is still the possibility of some response to the higher energy dissipation experienced by cells at 120 rpm, like the decrease in the maximum cell concentration, which, along with metabolic impact, are expected to be non-lethal responses. The widely used conditions for suspended CHO cell cultures in shake flasks presented in this work are suitable. However, at the lower shaking frequency and higher filling volumes, the risk of getting mass transfer limited is present, whereas at the higher shaking frequency of 120 rpm and the lower non-lethal responses to shear stress may be present.