spherical “cell” with a mammalian metabolism, 70% in- tracellular water, and a hydrated mass of 3,000 pg—roughly in the middle of the size range for mammalian cells.28Noting that suspension culture is28And larger than CHO cells, which are 1,000–2,000 pg wet [85]. likely to be the lowest-cost option for bulk cell growth,29it is further assumed29To be discussed from a bioreactor design perspective in Section 2.3. 13 /m.sc/o.sc/d.sc/e.sc/l.sc /c.sc/e.sc/l.sc/l.sc /c.sc/h.sc/a.sc/r.sc/a.sc/c.sc/t.sc/e.sc/r.sc/i.sc/s.sc/t.sc/i.sc/c.sc/s.sc 14 T/a.sc/b.sc/l.sc/e.sc 2.1 : Constituent composition for animal cell mass (dry CHON basis). C-formula HfGfWt% mol/mol kJ/mol Lipid CH 2O0.13[Palmitate] −54.0 −17.8 15% 0.205 Carbohydrate CH 2O −205 −147 10% 0.073 RNA/DNA CH 1.13O0.74N0.39[89] −119 −72.6 5% 0.036 Protein CH 1.57O0.31N0.28[90] −62.2 −21.7 70% 0.686 Overall (DCM a) CH 1.68O0.34N0.21 −73.0 −31.9 that the cell line has been adapted for suspension culture, much like CHO cells. If suspended cells are assumed to be spherical and to have a density of 1.03, then this mass resolves to a diameter of 18 m. Cell growth proceeds in the usual way with a maximum growth rate max=0.029/h, equivalent to a doubling time of 24 h.30On a bulk-mass basis, if a culture is gaining mass30See Note 8 for a description of “usual” cell growth. then it must be consuming mass (i.e., nutrients and O2) at a rate consistent with some growth stoichiometry.31If the culture is alive but not gaining mass,31To be discussed in Section 2.2.then it must still be consuming nutrients for maintenance. ACHONformulaforanimaldrycellmass(DCMa)ofCH1.68O0.34N0.21isde- rived in Table 2.1 from an average composition of a mammalian cell [86] and representative CHON formulas of constituent macromolecules.32Enthalpies32Forpurposesofthisanalysis,sulfur,phos- phorous, and metals are ignored. Addi- tionally, the typically cited 5–10% weight fraction of intracellular small metabolites isassumedtohaveacompositionreﬂective of the macromolecular composition and is thus normalized out.of formation ( Hf) for the constituent macromolecules and cell mass were estimated from the C-formulas and the correlation of Burnham [87]. En- tropies of formation ( Sf) were estimated with the correlation of Battley [88]. From these values, Gibbs free energies of formation ( Gf) were estimated at a reference temperature of 298 K.33 33Gf=HfTSfNote that choice of cell size does not have a signiﬁcant eﬀect on process economics, provided that cell- and number-speciﬁc quantities are converted to a mass basis. In particular, cell number density (in, e.g., million cells per mL or 106/mL) is a commonly reported quantity.34Errors in techno-34As are cell-speciﬁc rates of protein pro- duction, oxygen uptake, media perfusion, etc.economic assumptions can be introduced if a number density reported for a culture of a given cell size is applied to a cell of a diﬀerent size. Consider the practical maximum cell density in suspension culture, which occurs at a broth viscosity of ~2 cp. The Krieger-Dougherty model (Equation 2.1) can be used to estimate the viscosity of a suspension as a function of the volume fraction occupied by particles.35 35Here,0is the native liquid viscosity (~0.8 cp for cell-culture media at 37C) and max=0.65, an appropriate packing limit for soft spheres [91]. 0.0 0.1 0.2 0.3 0.4 0.5 Volume fraction () 0246810Relative viscosity (/0) =0= 1 max2.5 max (2.1) Allowing for additional viscosity contributions from growth-factor and extra- cellular proteins, a limiting volume fraction of cells can be taken as ~0.25. Viscosity increases sharply above this limit, as cell-cell collisions become more frequent. Indeed, microscopy of CHO cells (Figure 2.1) shows that cells are /s.sc/t.sc/o.sc/i.sc/c.sc/h.sc/i.sc/o.sc/m.sc/e.sc/t.sc/r.sc/y.sc /o.sc/f.sc /a.sc/n.sc/i.sc/m.sc/a.sc/l.sc /c.sc/e.sc/l.sc/l.sc /g.sc/r.sc/o.sc/w.sc/t.sc/h.sc 15 crowded on the slide at 20% volume fraction. At 30%, the cells are fully stacked on one another. Table 2.2 tabulates number and mass densities for various cell sizes at the viscosity limit of =0.25. While the attainable number density changes with cell size, the attainable mass density is invariant. Thus, to contextualize some cell-density assumptions in cultured-meat TEA, a “conservative” assumption of 40×106/mL for a cell size approaching 4,500 pg [13] is in fact much closer to the viscosity limit than a “challenging” assumption of 128 ×106/mL for a cell size of 1,000 pg [4]. To avoid ambiguity in later calculations, cell density is reported on both a number basis and a wet mass basis. 10% 20% 30% F/i.sc/g.sc/u.sc/r.sc/e.sc 2.1 : Phase-contrast microscopy of CHO cell suspensions at 10–30% volume fraction [91].T/a.sc/b.sc/l.sc/e.sc 2.2 : Attainable number and mass density at volume fraction =0.25 for various cell sizes. Speciﬁc O 2uptake rates predicted by Reaction 2.9 are also shown. Wet mass Diam. Max. density Speciﬁc OUR pg/cell m106/mL g/L wet pmol O 2/cell-h mg O 2/g-h 1,000 12.3 258 258 0.178 5.68 2,000 15.5 129 258 0.299 4.78 3,000 17.7 86 258 0.405 4.32 4,000 19.5 64 258 0.502 4.02 5,000 21.0 52 258 0.594 3.80 2.2Stoichiometry of animal cell growth Thestoichiometryoflifeisthesumofanabolism,growth-associatedcatabolism, and maintenance-associated catabolism [92]. Anabolism, or biosynthesis, describes the formation of complex molecules from simple ones. Catabolism provides the energy required to perform anabolism and maintain organismal function. Industrial fermentation processes are typically designed to provide a single carbon source, a single inorganic nitrogen source (ammonia or metal nitrate), a small amount of phosphate, and very small amounts of sulfur and trace metals. In most fermentations, cells also use the carbon source for energy. Animal cells, however, evolved to take energy and structural carbon from carbohydrates and fats, and organicnitrogen from digested protein, i.e., amino acids. They also evolved to take chemical signaling cues (including whether to live or die) from outside the cell. In addition to sugar (glucose), animal cell-culture media thus contain up to 20 essential and non-essential amino acids, fatty acids, phosphate, trace minerals, and various vitamins, hormones, and cytokines (collectively known as growth factors). From this wide array of nutrients, Xie and Zhou [90] provide some char- acteristics of ideal growth stoichiometry: •Glucose is utilized solely for energy production and the synthesis of lipids, structural carbohydrates, and nucleotides. •Glucose catabolism for energy production is completely oxidative: no lactate is produced. •The amino acid glutamine is utilized solely for protein and nucleotide synthesis. /s.sc/t.sc/o.sc/i.sc/c.sc/h.sc/i.sc/o.sc/m.sc/e.sc/t.sc/r.sc/y.sc /o.sc/f.sc /a.sc/n.sc/i.sc/m.sc/a.sc/l.sc /c.sc/e.sc/l.sc/l.sc /g.sc/r.sc/o.sc/w.sc/t.sc/h.sc 16 •Other amino acids are utilized for protein synthesis only. •No amino acids are catabolized. The degree to which cells adhere to these idealities depends on the instanta- neous culture environment as well as their speciﬁc metabolic wiring. These factors give a cell “options” for managing its metabolism. Excess glucose may be catabolized to lactate. Excess amino acids, particularly glutamine, may be catabolized to ammonia. At suﬃciently high concentration, either catabo- lite will inhibit cell growth. In principle, if the concentrations of all media components (along with O2, CO2, pH, temperature, etc.) could be controlled dynamicallyandindependentlyincellculture,theoptionscouldbeeliminated and these idealities could be realized. To that end, metabolic engineering is usually employed to predict and/or manipulate a given cell’s nutrient uptake rates and thereby gain a level of control over the culture [93]. In practice, this is not so easily achieved—even well-studied, workhorse CHO lines do not have ideal metabolisms, despite decades of incremental progress [90]. Process limitations associated with nonideality need to be considered at scale. ÉA/n.sc/a.sc/b.sc/o.sc/l.sc/i.sc/s.sc/m.sc The anabolic reaction for 1 mole of DCMa(Table 2.1) can be divided into subreactions for the constituent components.36The lipid fraction, which36Abbreviations, CHON formulas, and for- mation energies for the components ap- pearing in the following reactions can be found in Appendix B.comprises cellular membranes, is assumed to be synthesized from glucose (Glc):37 37Cellular lipids can also be partially syn- thesized from exogenous fatty acids (e.g., palmitate) [94], but these can be ex- pensive to isolate and reﬁne from plant sources. Further, choline and inositol are required vitamins for lipid synthesis, but are consumed at rates too low to appear in an overall stoichiometry [90].0.049 Glc!0.205 Lipid +0.090 CO2+0.090 H2O H=11.9 kJ=molG=14.6 kJ=mol(2.2) The carbohydrate (polysaccharide) fraction is synthesized by glucose poly- merization: 0.012 Glc!0.073 Carbohydrate H=0.4 kJ=molG=0.4 kJ=mol(2.3) In a simpliﬁed view [95], nucleotide synthesis is carried out with carbon from glucose and only one of the N atoms on glutamine (Gln), rejecting glutamate (Glu). After balancing N, glucose balances the reaction:38 38Note that the apparent CO 2requirement in Reaction 2.4 is more than satisﬁed by the CO 2generated in Reaction 2.2. 0.004 Glc +0.014 Gln +0.014 CO2! 0.036 RNA=DNA +0.014 Glu +0.009 H2O H=1.0 kJ=molG=1.5 kJ=mol(2.4) /s.sc/t.sc/o.sc/i.sc/c.sc/h.sc/i.sc/o.sc/m.sc/e.sc/t.sc/r.sc/y.sc /o.sc/f.sc /a.sc/n.sc/i.sc/m.sc/a.sc/l.sc /c.sc/e.sc/l.sc/l.sc /g.sc/r.sc/o.sc/w.sc/t.sc/h.sc 17 Finally, the formula for protein in Table 2.1 was derived from an average amino acid proﬁle of 207 cellular proteins [90]. The anabolic reaction for forming this protein is the sum of the individual amino acids in the correct ratios: 0.007 Arg +0.004 Cys +0.006 Gln +0.003 His +0.007 Ile +0.010 Lys +0.002 Met +0.005 Phe +0.009 Thr +0.002 Trp +0.005 Tyr +0.010 Val +0.013 Ala +0.006 Asn +0.008 Asp +0.009 Glu +0.011 Gly +0.011 Leu +0.007 Pro +0.010 Ser!0.686 Protein (CH1.57O0.31N0.28) +0.142 H2O H=2.9 kJ=molG=9.9 kJ=mol(2.5) For cell mass growth from individual amino acids, the following anabolic reaction (the superposition of Reactions 2.2–2.5) is used throughout the analysis: 0.065 Glc +0.007 Arg +0.004 Cys +0.020 Gln +0.003 His +0.007 Ile +0.010 Lys +0.002 Met +0.005 Phe +0.009 Thr +0.002 Trp +0.005 Tyr +0.010 Val +0.013 Ala +0.006 Asn +0.008 Asp +0.011 Gly +0.011 Leu +0.007 Pro +0.010 Ser!DCMa+0.005 Glu +0.076 CO2+0.240 H2O H=7.5 kJ=molG=2.8 kJ=mol(2.6) ÉW/i.sc/l.sc/d.sc-/t.sc/y.sc/p.sc/e.sc /c.sc/a.sc/t.sc/a.sc/b.sc/o.sc/l.sc/i.sc/s.sc/m.sc As is evident in the subreactions, anabolism uses no oxygen and has a small to negligible reaction energy. Cell growth is an irreversible process, however, and Gibbs free energy must be dissipated during growth. This Gis captured by the catabolic reaction. Experimentally, the sensible heat (enthalpy, H) dissipated during cell growth can be measured with calorimetry, then con- verted to a Gdissipation by correcting for the entropy change.39Guan and39Decades of such experiments for indus- trial microbes have generated an array of engineering correlations describing fer- mentation energetics for ﬁrst-principles process design [88, 96–98]. Only limited examples exist in the literature of similar calorimetric experiments on animal cell cultures [99, 100]. This line of investiga- tion seems to have lost steam ~20 years ago, probably in favor of metabolic ﬂux analysis and omics techniques.Kemp measured the enthalpy dissipation in a batch CHO culture producing interferon (IFN- ) along with lactate (Lac), CO2, and NH3[101]. At diﬀerent times in the batch, the authors deduced anabolic and catabolic reactions that matched the formation rates of products and cells as well as the observed heat dissipation. Reaction 2.7 was deduced at the end of the batch, when the culture was in decline and no further anabolism was taking place: 1.0 Glc +0.13 Gln +1.28 O2! 0.26 NH3+1.77 Lac +1.34 CO2+0.95 H2O H=681 kJ=molG=700 kJ=mol(2.7) Reaction 2.7 has a few notable aspects. First, its HrandGrare reason- ably similar, i.e., the Gibbs energy of cell growth is mostly dissipated as heat rather than as entropy. This means that calorimetry measurements (of en- thalpy) do not need signiﬁcant correction for entropy. Second, for suﬃciently /s.sc/t.sc/o.sc/i.sc/c.sc/h.sc/i.sc/o.sc/m.sc/e.sc/t.sc/r.sc/y.sc /o.sc/f.sc /a.sc/n.sc/i.sc/m.sc/a.sc/l.sc /c.sc/e.sc/l.sc/l.sc /g.sc/r.sc/o.sc/w.sc/t.sc/h.sc 18 slow growth, it can be assumed that maintenance-associated catabolism is much larger than growth-associated catabolism; therefore this reaction primarily represents the former. Finally, this reaction appears to be a super- position of respiration, glycolysis, and some form of glutamine catabolism, e.g., glutaminolysis [102]. On a basis of one mole glucose, Reaction 2.7 can thus be speciﬁed with two degrees of freedom.40For example, as written, it40These can be thought of as the metabolic “options” discussed above. has a lactate/glucose ratio (Lac/Glc) of 1.77 and glutamine/glucose ratio (Gln/Glc) of 0.13. With the Hrof anabolism being nearly zero, it can be assumed that the catabolic reaction proceeds at a rate that meets an observed sensible heat dissipation. Guan and Kemp [101] reported an enthalpy dissipation (metabolic power) in CHO culture of 22–25 pW/cell. In similar experiments on mouse hybridoma, they reported a metabolic power of ~34 pW/cell. West et al. [103] noted that this result is general: across all mammalian species, cells of similar size (e.g., CHO cells and hybridomas) have similar metabolic powers in vitro. West et al. further showed that in vitro metabolic power PM can be scaled to hydrated cell mass with a 3/4 exponent:41 41PMcan also be thought of as the basal metabolic rate of the cell. For CHO cells of 1,167 pg (350 pg dry mass [85] and 70% intracellular water), the correlation of West et al. indeed predicts 30 pW/cell.PM=0.148 M0.75 c(PMin pW, Mcin pg ) (2.8) In West’s relation, cells with wet mass 3,000 pg have a PMof 60 pW, requiring that Reaction 2.7 proceed at 0.0077 mol/mol DCMa-h. An overall reaction that describes a wild-type metabolism can be obtained by assuming=0.029/h and combining the anabolic and catabolic contribu- tions into a single reaction in mol/mol DCMa-h:42 42Note that glutamate is produced by Re- action 2.4 in excess of what is required in Reaction 2.5. 0.333 Glc +0.342 O2+0.007 Arg +0.004 Cys +0.055 Gln +0.003 His +0.007 Ile +0.010 Lys +0.002 Met +0.005 Phe +0.009 Thr +0.002 Trp +0.005 Tyr +0.010 Val +0.013 Ala +0.006 Asn +0.008 Asp +0.011 Gly +0.011 Leu +0.007 Pro +0.010 Ser! DCMa+0.005 Glu +0.070 NH3+0.474 Lac +0.435 CO2+0.495 H2O H=190 kJ=molG=190 kJ=mol(2.9) The amino acids in Reaction 2.9 can be divided into essential amino acids (EAA) that must be supplied in culture media and a non-essential remainder (NAA)thatcanbesynthesizedfromotheravailableaminoacidsifnotprovided in media. At the bench scale, pre-formulated, deﬁned medium DMEM/F12 is a good starting point for serum-free animal cell culture. DMEM/F12 has a general-use amino acid proﬁle that must be supplemented with glu- tamine (which is not shelf-stable in solution) and any other deﬁcient amino acids [104]. To validate the stoichiometry of Reaction 2.9 against that supplied in DMEM/F12,43Figure 2.2 compares their relative macronutrient proﬁles. With43High glucose, with glutamine and stan- dard supplementation [105]. Note that amino acid hydrates/hydrochlorides, etc. were normalized to the pure formula.respect to glucose and the essential amino acids, the proﬁles compare quite favorably, requiring only minor supplementation of cysteine and tryptophan. /s.sc/t.sc/o.sc/i.sc/c.sc/h.sc/i.sc/o.sc/m.sc/e.sc/t.sc/r.sc/y.sc /o.sc/f.sc /a.sc/n.sc/i.sc/m.sc/a.sc/l.sc /c.sc/e.sc/l.sc/l.sc /g.sc/r.sc/o.sc/w.sc/t.sc/h.sc 19 Glc Arg Cys Gln His Ile Lys Met Phe Thr Trp Tyr Val Ala Asn Asp Glu Gly Leu Pro Ser0.1%1%10%100%Component wt%Essential Non-essentialCellular stoich. DMEM/F12 F/i.sc/g.sc/u.sc/r.sc/e.sc 2.2 : Macronutrient proﬁle of Reaction 2.9 compared to that supplied by DMEM/F12. DMEM/F12 would be deﬁcient in several non-essential amino acids, but these could be supplemented with some level of art, based on cost and eﬃciency of uptake and synthesis. The cell-speciﬁc oxygen uptake rate (SOUR), given in Table 2.2 for var- ious cell sizes, provides a further validation of the growth stoichiometry of Reaction 2.9. For CHO cells (~1,000–2,000 pg), the reported SOUR is 0.25– 0.30 pmol O2/cell-h [106]. At a growth rate of =0.029/h, the SOUR pre- dictedbyReaction2.9isingoodagreementwiththisvalue(0.30pmolO2/cell- h for a 2,000 pg cell). Also note from Table 2.2 that the choice of cell mass aﬀects both the cell-speciﬁc and the mass-speciﬁc rate of catabolism through Equation 2.8. The baseline mass of 3,000 pg was thus chosen to fall in the middle of the likely metabolic range. ÉE/n.sc/h.sc/a.sc/n.sc/c.sc/e.sc/d.sc /c.sc/a.sc/t.sc/a.sc/b.sc/o.sc/l.sc/i.sc/s.sc/m.sc Reactions 2.7 and 2.9 were given a “wild-type” designation and stand in for an unoptimized, ineﬃcient cell line. The high lactate/glucose ratio and overactive glutamine metabolism in Reaction 2.7 are manifestations of a larger metabolic phenomenon known as the Warburg eﬀect [102]. This phenomenon is a hallmark of rapidly proliferating animal cells, including CHO cells in culture and cancer cells in general. The cells choose to route glucose through glycolysis even when ample O2for respiration is provided, andtocatabolizeaminoacidsforenergyevenwhenampleglucoseisprovided. The Warburg eﬀect is poorly understood; a prevailing hypothesis holds that it allows glycolysis and TCA-cycle intermediates from glucose and glutamine to be used in anabolism for rapid accumulation of biomass. Carbon-labeling experiments have shown that high availability of such intermediates is indeed important for fast growth, but the intermediates do not themselves end up as biomass carbon [94]. Either way, it seems likely44that an assumption of high 44And perhaps thermodynamically intu- itive. metabolic eﬃciency is inconsistent with an assumption of high growth rate. /s.sc/t.sc/o.sc/i.sc/c.sc/h.sc/i.sc/o.sc/m.sc/e.sc/t.sc/r.sc/y.sc /o.sc/f.sc /a.sc/n.sc/i.sc/m.sc/a.sc/l.sc /c.sc/e.sc/l.sc/l.sc /g.sc/r.sc/o.sc/w.sc/t.sc/h.sc 20 In Section 2.3, however, it will be demonstrated that the lactate and ammonia generation rates of Reaction 2.9 preclude this stoichiometry from reaching an economically high cell density. In biopharmaceutical cell culture, there are several strategies for optimizing growth stoichiometry through cell- linecharacterizationandengineering. Theseinclude: selectionforphenotypes withlactatereuptakecapability;45geneticmodiﬁcationtoexpressaglutamine45Aerobic catabolism of Lac.synthetase enzyme;46and feedback control of glucose concentration and 46Intracellular synthesis of Gln from Glu and NH 3.pH [107, 108]. The end result of such metabolic enhancements is diﬃcult to forecast at this stage of analysis, but Reaction 2.10 stands for an enhanced catabolism, with Lac/Glc=0.50 and Gln/Glc=0.025:47 47The reasoning for these parameters will become clear in Section 2.3. 1.0 Glc +0.025 Gln +4.61 O2! 0.050 NH3+0.50 Lac +4.63 CO2+4.55 H2O H=2,225 kJ=molG=2, 271 kJ=mol(2.10) For 60 pW/cell, this catabolism proceeds at 0.0024 mol/mol DCMa-h. The enhanced overall reaction is thus: 0.147 Glc +0.378 O2+0.007 Arg +0.004 Cys +0.022 Gln +0.003 His +0.007 Ile +0.010 Lys +0.002 Met +0.005 Phe +0.009 Thr +0.002 Trp +0.005 Tyr +0.010 Val +0.013 Ala +0.006 Asn +0.008 Asp +0.011 Gly +0.011 Leu +0.007 Pro +0.010 Ser! DCMa+0.005 Glu +0.004 NH3+0.041 Lac +0.455 CO2+0.613 H2O H=190 kJ=molG=189 kJ=mol(2.11) In the context of nutrient utilization, it is worth noting that Reaction 2.11 only reduces the amount of glucose and glutamine consumed in the growth of 1 mol DCMaby about 60% each over Reaction 2.9 (see Table 2.3). Even if full respiration were assumed, eliminating Lac and NH3entirely, the additional improvement is marginal. In either case, the relative O2uptake and CO2 generation rates are higherwith the more eﬃcient metabolism. These have implications for bioreactor design, to be discussed in Section 2.3.T/a.sc/b.sc/l.sc/e.sc 2.3 : Stoichiometric uptake (nega- tive) or generation (positive) per mole of DCMafor Reactions 2.9, 2.11, and full res- piration (hypothetical). 2.9 2.11 Full resp. Glc -0.33 -0.15 -0.13 Gln -0.05 -0.02 -0.02 O2-0.34 -0.38 -0.38 CO20.44 0.46 0.46ÉC/o.sc/m.sc/p.sc/l.sc/e.sc/x.sc /a.sc/m.sc/i.sc/n.sc/o.sc /a.sc/c.sc/i.sc/d.sc /s.sc/o.sc/u.sc/r.sc/c.sc/e.sc/s.sc At the hypothetical scale of cultured meat, plant protein hydrolysates may be more cost-eﬀective and sustainable than amino acids produced individually by fermentation. Figure 2.3 presents conceptualized material and energy ﬂows in a cultured-meat future, beginning from sunlight, CO2, and fossil fuel.48These fundamental sources, and the plants produced from them, are48Former sunlight and CO 2.already available at scales ranging from huge to practically inﬁnite. Similarly, as a byproduct of soybean oil extraction, soybean meal is already produced at extremely large volumes and is currently used as animal feed. Assuming a reduced-animal future where soybeans are still grown for oil, new outlets will have to be found for this material. /s.sc/t.sc/o.sc/i.sc/c.sc/h.sc/i.sc/o.sc/m.sc/e.sc/t.sc/r.sc/y.sc /o.sc/f.sc /a.sc/n.sc/i.sc/m.sc/a.sc/l.sc /c.sc/e.sc/l.sc/l.sc /g.sc/r.sc/o.sc/w.sc/t.sc/h.sc 21 Natural gasNatural gasCarbohydrate cropProtein cropHydrolysate Refined sugar MillingMillingPower plantPower plant Ammonia plantAmmonia plantOilseed millOilseed mill Growth factors Amino acidsHydrolysisHydrolysis Cell cultureCell culture FermentationFermentationMeal Ferm. nutrientFertilizerSun + CO 2+ refining + refiningCell mass F/i.sc/g.sc/u.sc/r.sc/e.sc 2.3 : Material ﬂows upstream of the cell-culture facility, starting from sunlight, CO 2, and natural gas. Figure2.4comparestheamino-acidproﬁleoftheproteinsynthesisreaction (2.5) to that of U.S. soybean meal [109]. The EAA proﬁles are similar enough that if a quantitative hydrolysate of soybean meal were fed at 1.36 mol per mol protein,49all EAA requirements could be met except for glutamine49To match on threonine.(which must be fed separately in any case) and about 75% of tyrosine.50With 50Soybeans are not the only nitrogen-rich crop; peas and other legumes could also be used, as could extracts of yeast or in- deed algae [14]. Conceivably, a blend of hydrolysates could be designed to fully re- place all exogenous amino acids (with the probable exception of Gln) in cell-culture media without supplementation.aggregate compounds standing for the soy hydrolysate and the unused amino- acid fraction (including Glu formed in Reaction 2.4), the following alternate reactions can be derived. With the wild-type catabolism of Reaction 2.7: 0.333 Glc +0.342 O2+0.055 Gln +0.004 Tyr +0.192 Soy Hydr. (C4.81H9.49O2.68N1.28)! DCMa+0.070 NH3+0.474 Lac +0.435 CO2+0.495 H2O +0.142 Unused AA (C2.63H4.86O1.75N0.60) H=197 kJ=molG=205 kJ=mol(2.12) And with the enhanced catabolism of Reaction 2.10: 0.147 Glc +0.378 O2+0.022 Gln +0.004 Tyr +0.192 Soy Hydr. (C4.81H9.49O2.68N1.28)! DCMa+0.004 NH3+0.041 Lac +0.455 CO2+0.613 H2O +0.142 Unused AA (C2.63H4.86O1.75N0.60) H=197 kJ=molG=204 kJ=mol(2.13) /b.sc/i.sc/o.sc/r.sc/e.sc/a.sc/c.sc/t.sc/o.sc/r.sc /d.sc/e.sc/s.sc/i.sc/g.sc/n.sc /p.sc/r.sc/i.sc/n.sc/c.sc/i.sc/p.sc/l.sc/e.sc/s.sc /a.sc/n.sc/d.sc /l.sc/i.sc/m.sc/i.sc/t.sc/a.sc/t.sc/i.sc/o.sc/n.sc/s.sc 22 Arg Cys Gln His Ile Lys Met Phe Thr Trp Tyr Val Ala Asn Asp Glu Gly Leu Pro Ser0.000.050.100.150.200.25Moles of amino acidEssentialNon-essentialCellular protein (1 mol) U.S. soybean meal (1.36 mol) F/i.sc/g.sc/u.sc/r.sc/e.sc 2.4 : Amino-acid proﬁles of cellular protein (Reaction 2.5) and U.S. soybean meal. 2.3Bioreactor design principles and limitations Section 2.1 established practical upper limits for attainable cell density as dictated by a maximum suspension viscosity. Whether or not a given bioreac- tor can support this viscosity-limited cell density depends on its capacity for oxygen transfer, its characteristic mixing eﬃciency, the rate of inhibitor accu- mulation, and other factors. For example, the conceptual process of van der Weele and Tramper [4] considered a 20 m3stirred-tank bioreactor (STR) as the ﬁnal production vessel, operating in fed-batch mode with a ﬁnal cell den- sity of 128 ×106/mL.51Individually, this bioreactor volume and cell density51At their assumed cell size of 1,000 pg, this is equivalent to a mass density of 128 g/L, or about halfway to the viscos- ity limit.are at or near world-record levels (at least for CHO culture), though a combi- nation of the two extremes has not been reported. In suspended CHO culture, typicalfed-batchcelldensitiesarerathercloserto10 ×106–30×106/mLatany volume, which is suﬃcient for protein production at modern titers [110]. Cell densities on the order of 100 ×106/mL are more consistent with high-density perfusion cultures. JacketJacket TD=T/3 SpargerH = 2 T 0.8 H F/i.sc/g.sc/u.sc/r.sc/e.sc 2.5 : Schematic of a stirred-tank bioreactor (STR) with external cooling jacket. The bioreactor diameter is denoted T(for “tank”) and impeller diameter D.Figure 2.5 presents a sketch of an STR with construction aspect ratio H/T of 3, two rotating impellers of diameter D=T/3, and a ﬁnal working volume of 80%. In a bubble-column or airlift bioreactor, the aspect ratio is generally higher ( H/T=6–10) and no impeller is present. Gas bubbles are used to transfer O2into solution and strip CO2out in all large bioreactor designs (>~1 m3). If the bioreactor is equipped with an impeller, the stirring action can be used to enhance this gas-liquid mass transfer. Stirring and sparging are thus the main operational degrees of freedom in a bioreactor. The gas sparge rate is usually quantiﬁed in terms of vvm (standard volumes of sparge gas per volume of liquid per minute) or superﬁcial velocity us(m/s, the actual volumetric ﬂow rate of gas divided by the bioreactor cross-sectional area). The stirring or agitation rate is usually quantiﬁed as power input per unit of liquid volume ( P/V, in W/m3) or per unit of liquid mass ( ¯"=P/V, in W/kg.) /b.sc/i.sc/o.sc/r.sc/e.sc/a.sc/c.sc/t.sc/o.sc/r.sc /d.sc/e.sc/s.sc/i.sc/g.sc/n.sc /p.sc/r.sc/i.sc/n.sc/c.sc/i.sc/p.sc/l.sc/e.sc/s.sc /a.sc/n.sc/d.sc /l.sc/i.sc/m.sc/i.sc/t.sc/a.sc/t.sc/i.sc/o.sc/n.sc/s.sc 23 Inspargedbioreactors,cellsinsuspensiontendtoattachtoarisingbubble’s exterior or get dragged in its wake. If cells are too close to the bubble when it ultimately bursts at the top of the bioreactor, they will incur high shear forces. Due to their larger size and lack of a rigid cell wall, animal cells are particularly susceptible to these forces, which can cause physiological changes including death [52]. Under practical cell-culture conditions, bubble- induced shear forces are orders of magnitude higher than shear forces from a rotating impeller. Consensus in the literature therefore holds that the threat of shear from agitation is probably overstated,52while that from bursting and52For suspension culture but not necessar- ily for microcarrier culture. collapsing bubbles is real [111]. Gas sparging in animal cell culture is thus used judiciously.53 53A common feature of record-high- density animal cell cultures is that they are not sparged at all, with O 2instead sup- plied via the bioreactor headspace [112, 113].Judicious sparging rules out the bubble-column bioreactor, which has not been successfully used for animal cell culture beyond the bench scale. The airlift reactor with a liquid downcomer has been used for low-density cell culture up to 10 m3, though much smaller reactors of 1–2 m3are more common. At larger scale, O2depletion in the ungassed downcomer can become prohibitive [114].54Gently sparged STRs are thus preferred. Physical54Li et al. [115] oﬀered a CFD model of a hypothetical 300 m3airlift reactor for CHO cell culture. Their simulations in- dicated 46% (3.2 mg/L) dissolved O 2at the top of the sparged column, about half of which was consumed by cells during a 20-second trip through the downcomer. Uponreview,however,IﬁndthattheSOUR assumed in the simulation was only half of what was actually observed in the au- thors’ own reference [116], and 20% of that predicted by Reaction 2.9 and other