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Scale-Up Economics for Cultured Meat: Techno-Economic Analysis and Due Diligence

Authors:
  • DWH Process Consulting

Abstract and Figures

“Cultured meat” technologies aim to replace conventional meat with analogous or alternative bioproducts from animal cell culture. Developers of these technologies claim their products, also known as “cell-based” or “cultivated” meat, will be safer and more environmentally friendly than conventional meat while offering improved farm-animal welfare. To these ends, Open Philanthropy commissioned this assessment of cultured meat’s potential to measurably displace the consumption of conventional meat. Recognizing that the scalability of any cultured-meat products must in turn depend on the scale and process intensity of animal cell production, this study draws on techno-economic analysis and due-diligence perspectives in industrial fermentation and upstream biopharmaceuticals to assess the extent to which animal cell culture could be scaled like a fermentation process. The analysis identifies a number of significant barriers to the scale-up of animal cell culture. Bioreactor design principles indicate a variety of issues associated with bulk cell growth in culture: Low growth rate, metabolic inefficiency, catabolite and CO2 inhibition, and bubble-induced cell damage will all limit practical bioreactor volume and attainable cell density. With existing bioreactor designs and animal cell lines, a significant engineering effort would be required to address even one of these issues. Economic challenges are further examined. Equipment and facilities with adequate microbial contamination safeguards are expected to have high capital costs. Suitable formulations of amino acids and protein growth factors are not currently produced at scales consistent with food production, and their projected costs at scale are likewise high. The replacement of amino-acid media with plant protein hydrolysates is discussed and requires further study. Capital- and operating-cost analyses of conceptual cell-mass production facilities indicate production economics that would likely preclude the affordability of their products as food. The analysis concludes that metabolic efficiency enhancements and the development of low-cost media from plant hydrolysates are both necessary but insufficient conditions for the measurable displacement of conventional meat by cultured meat.
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Scale-Up Economics
for Cultured Meat
Techno-Economic Analysis
and Due Diligence
David Humbird
DWH Process Consulting LLC
Centennial, Colorado USA
Prepared for Open Philanthropy
San Francisco, California USA
December 28 2020
Revision 3: October 4 2021
Executive Summary
“Cultured meat” technologies aim to replace conventional meat with analogous
or alternative bioproducts from animal cell culture. Developers of these
technologies claim their products, also known as “cell-based” or “cultivated”
meat, will be safer and more environmentally friendly than conventional
meat while offering improved farm-animal welfare. To these ends, Open
Philanthropy commissioned this assessment of cultured meat’s potential to
measurably displace the consumption of conventional meat.
Recognizing that the scalability of any cultured-meat products must in
turn depend on the scale and process intensity of animal cell production, this
study draws on techno-economic analysis and due-diligence perspectives in
industrial fermentation and upstream biopharmaceuticals to assess the extent
to which animal cell culture could be scaled like a fermentation process.
The analysis identifies a number of significant barriers to the scale-up of
animal cell culture. Bioreactor design principles indicate a variety of issues
associated with bulk cell growth in culture: Low growth rate, metabolic
inefficiency, catabolite and CO
2
inhibition, and bubble-induced cell damage
will all limit practical bioreactor volume and attainable cell density. With
existing bioreactor designs and animal cell lines, a significant engineering
effort would be required to address even one of these issues.
Economic challenges are further examined. Equipment and facilities with
adequate microbial contamination safeguards are expected to have high
capital costs. Suitable formulations of amino acids and protein growth factors
are not currently produced at scales consistent with food production, and their
projected costs at scale are likewise high. The replacement of amino-acid
media with plant protein hydrolysates is discussed and requires further study.
Capital- and operating-cost analyses of conceptual cell-mass production
facilities indicate production economics that would likely preclude the af-
fordability of their products as food. The analysis concludes that metabolic
efficiency enhancements and the development of low-cost media from plant
hydrolysates are both necessary but insufficient conditions for the measurable
displacement of conventional meat by cultured meat.
Analysis highlights
Bioreactor design and scale-up principles are used to examine practical vol-
umes and attainable cell densities in fed-batch and perfusion suspension
cultures.
Equipment costs consistent with appropriate levels of sterility assurance and
commoditization are developed with process-industry estimation software
and cost-factor techniques.
ii
iii
Price-volume relationships are leveraged for demand-consistent forecasting of
amino acid and protein prices in cell-culture media. The costs and suitability
of speculative plant hydrolysates as cell-culture media are also considered.
Process designs and production cost estimates are developed for conceptual
fed-batch and perfusion facilities producing bulk animal cell mass within a
total market of 100 kTA (wet basis). Both are examined in the context of a
cellular metabolism significantly enhanced over a wild-type animal cell.
A fed-batch facility of 24×20 m
3
bioreactors is estimated to produce 6.8 kTA
of wet cell mass at a production cost of $37/kg. Amino acids contribute 50%
of this cost. Clean room costs limit the size of a single facility, while CO
2
accumulation limits the volume of the production bioreactor.
A perfusion facility of 96×2 m
3
bioreactors is estimated to produce 6.9 kTA
of wet cell mass at a production cost of $51/kg. The economics of perfusion
are disadvantaged by the high installation costs of small bioreactors and the
extra capital and consumables costs associated with the perfusion device.
Both estimates exceed a price target of $25/kg wet cell mass asserted for
consistency with 100 kTA consumption. Low-cost plant hydrolysate at $2/kg
could reduce all production cost estimates by $15–16/kg. A fed-batch process
with hydrolysate media would thus fall below $25/kg. Lower-grade mate-
rials of construction, elimination of clean rooms, and additional metabolic
enhancement offer smaller reductions.
With either technology, reduced metabolic efficiency leads to catabolite-limited
cell densities that cause the modeled production cost to increase beyond
economically sustainable levels.
Supplemental information
An Excel spreadsheet containing the calculations in this analysis can be down-
loaded at https://doi.org/10.17605/OSF.IO/AJSU9.
List of Revisions
1. December 28, 2020: Initial upload
2. December 30, 2020:
Added a DOI link to the Excel spreadsheet.
Fixed one typo.
3. October 4, 2021:
Added this list.
Added a/b markings to Fig. 1.2.
Fixed incorrect “ISBL Direct Cost” reference in Tables 4.3 and 4.10.
No changes to final costs or conclusions.
Clarified captions on Tables 4.4 and 4.11. Added distinct columns
for global and per-plant nutrient demands. Corrected units on
micronutrients in 4.11. No changes to final costs or conclusions.
Fixed typos and the placement of Table 1.3.
iv
Contents
executive summary ii
list of revisions iv
contents v
1 introduction 1
1.1 Background ................................. 1
1.2 Industrial scale-up perspectives . . . . . . . . . . . . . . . . . . . . . 3
1.3 Analysis approach: powers of ten . . . . . . . . . . . . . . . . . . . . 9
2 technical aspects 13
2.1 Model cell characteristics . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2 Stoichiometry of animal cell growth . . . . . . . . . . . . . . . . . 15
2.3 Bioreactor design principles and limitations . . . . . . . . . . . . 22
2.4 Aseptic operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3 economic aspects 34
3.1 Capitalcosts................................ 34
3.2 Costs of media components . . . . . . . . . . . . . . . . . . . . . . 39
3.3 Fixed operating costs . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4 production cost studies 48
4.1 Fed-batch operation . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.2 Perfusion operation . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.3 Economic sustainability metrics . . . . . . . . . . . . . . . . . . . . 66
5 concluding discussion 70
5.1 Summary.................................. 70
5.2 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
5.3 Related topics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
acknowledgments 77
bibliography 78
a baker’s yeast analysis 89
b physical properties used in the analysis 99
v
1
Introduction
1.1 Background
“Cultured meat” refers to a nascent field of bioproducts that aim to replace
conventional meat produced by farming and slaughter with analogous or
alternative products made from edible animal cell culture.
1
In one concept
1
Alternatively, “lab-grown” or “in vitro”
meat, along with other terms. During the
preparation of this report, the preferred
term of art (according to consumer re-
search conducted by The Good Food In-
stitute) shifted from “clean” [1] to “cell-
based” [2] to “cultivated” meat [3]. For the
present discussion, “cultured” has been re-
tained as a neutral term indicating a prod-
uct of cell culture.
(Figure 1.1), animal cells from a live-animal biopsy are propagated through
a series of increasingly large bioreactors, growing in number with each step
and ultimately inoculating a 20 m
3
bioreactor [4]. After a total cycle time
lasting several months, 2–3 tons of animal cell slurry are harvested from
this bioreactor. The cultured cell mass, perhaps blended with vegetable
proteins and fats, can be further processed with enzymes
2
and conventional
2
E.g., transglutaminase AKA “meat glue”
[5].
extrusion/texturization operations into edible mincemeat- or nugget-style
food products. In Figure 1.1, these are indicated as “unstructured” products.
Some developers, probably sensing consumer and investor ambivalence to
such products [6,7], have further proposed that cultured animal cells be
deposited onto an edible scaffold material that provides form and possibly
hypertrophy, resulting in “structured” products that more closely resemble a
cut of meat from an animal.
To its proponents, cultured meat is positioned to address global prob-
lems associated with industrial animal farming, such as its contributions
to pollution, foodborne illness, and anthropogenic climate change [810].
The promises of cultured meat thus include resource-efficient production of
human nutrition at a global scale and reduction of livestock populations to
pre-industrial levels. At the heart of cultured meat’s conceptual appeal is
Cell
bank
Bulk cell production
Extrusion
Texturization
Blending
Differentiation
Scaffolding
Hypertrophy
Structured product
Unstructured product
Host animal biopsy
Cell line
development
Primary
cell culture
Figure 1.1: Conceptual cultured-meat production process.
1
background 2
the further promise that all of this could be accomplished without requiring
existing meat consumers to significantly change their diet [11]. In many
cases, however, these promises are contingent upon, e.g, concomitant major
advances in renewable energy [12], a wholesale “rethink” of the composition
and cost structure of cell-culture media [13], presumptive future feedstock
sources such as mass-cultivated algae or cyanobacteria [14], or a correction
to the consumer price of conventional meat that brings it up to parity with its
toll on the environment [15]. The consumer price of cultured meat, mean-
while, is unknown. The present analysis was therefore commissioned to assess
cultured meat’s potential to measurably displace the human consumption of
conventional meat.
The reader is likely familiar with Mark Post’s 2013 media event [16] in
which a ~$325,000 (250,000) lab-grown hamburger was presented to a
panel of food critics. This figure was computed by totaling Post’s direct costs
leading up to the event, including the wages of the scientists and technicians
who labored for some months to make the item [17]. In 2015, Post offered a
preliminary production-cost estimate for such products of $65/kg [18,19],
which some observers extrapolated to $11 per burger [20].
3
Subsequently,
3
In a historical aside, the original projec-
tion was “eighty dollars” per kg, which
resolves to $11 for a 5-oz burger. These
words, however, were not uttered by Post,
but by an Australian radio reporter [18]
and had likely been converted to AUD for
the audience. Later that week, it was re-
ported that Post had claimed a production
cost of USD 65/kg [19], consistent with
the exchange rate at the time.
this analyst has encountered bioproducts entrepreneurs and investors who
somehow inferred from these events that Post et al. were able to reduce the
cost of animal cell culture by five orders of magnitude in two years. The reader
may also be familiar with this sentiment regarding cultured meat, which is
expressed in the popular media through hopeful invocations of “Moore’s law”
and awed remarks about the steadily declining price of something that is not
available for purchase [2125]. Ultimately, however, there is no responsible
comparison to be made between these two costs. The lower figure was merely
ascale-up projection—an opaque one at that, as its details were not published
for examination.
The art of the scale-up projection is sometimes known as techno-economic
analysis (TEA). In the (bio)process industries, TEA leverages conceptual
process design, simulation, and equipment costing techniques to develop
estimates of the capital, operating, and total production costs
4
of technologies
4
CAPEX, OPEX, and COP (cost of produc-
tion).
at full scale, based on lab/pilot-scale performance and projected improve-
ments [26]. Referring to the conceptual cultured-meat process in Figure 1.1,
it can be concluded that the scalability of either class of products from cell
culture (structured or unstructured) depends on the scalability of the bulk cell
production step. As further indicated in Figure 1.1, there is an expectation
that this step would be carried out in large (
200 m
3
) stainless-steel tanks,
such that the production facility would resemble a large-scale fermentation
plant or perhaps a brewery [2730]. A nebulous precedent for this concept
comes from the biopharmaceutical industry, where therapeutic proteins are
produced from recombinant mammalian cell lines in (much smaller) stainless
steel bioreactors
5
of up to 20–25 m
3
. Drawing on techno-economic analysis
5
Terminology note: fermentor will be used
for microbial culture equipment; bioreac-
tor for animal cell-culture equipment.
and scale-up techniques from industrial biotechnology (biofuels, baker’s yeast,
commercial enzymes) as well as from conventional animal cell culture as car-
industrial scale-up perspectives 3
ried out in the biopharmaceutical industry, this analysis examines the extent
to which an animal cell-culture process could be scaled like a fermentation
process. Its ultimate goal is to provide a transparent scale-up projection of a
bulk cell-mass process that produces a new, commoditized starting material
for downstream processing into an array of meat substitutes. Technical and
economic aspects will be explored in detail so that scale-up challenges can
be well understood and discussed. To begin, perhaps some management of
expectations is in order.
1.2 Industrial scale-up perspectives
The promises of cultured meat may sound very familiar to erstwhile practi-
tioners of another modern biotechnology once seemingly destined to save the
planet: biofuels. In the 1990s and 2000s, many biotechnology developers
sought to leverage modern advances in metabolic engineering and recom-
binant DNA technology (together known as synthetic biology [3133]) to
produce fuels and chemicals in workhorse microbes like E. coli or S. cere-
visiae. With a few notable exceptions [34,35], however, the great promise
of synthetic biology for fuels and chemicals was largely waylaid by low-level
difficulties in engineering, scale-up, and cost-competitiveness.
(a)
(b)
Figure 1.2: 2000–2019 prices, unad-
justed and adjusted to 2018$, for (a) WTI
crude oil [36] and (b) fresh beef [37].
For U.S. developers in particular, the biofuels wager was twofold. First,
the price of oil would have to remain high—on the order of $100/barrel,
as was observed before and after the 2008 financial crisis (Figure 1.2a). A
high oil price would ensure the eventual cost-competitiveness of new biofuels
with petroleum incumbents and help drive interest and funding in biofuels
research in the meantime. Second, these new bioprocesses needed tremen-
dous potential to scale, that is, to operate in extremely large fermentors
and at a very high intensity. Scale-up presented biofuels process engineers
with several challenges. The metabolic pathways to the molecules of interest
generally required highly aerobic fermentations. Compared to an anaero-
bic process (e.g., ethanol production), aerobic fermentations generally have
a lower carbon efficiency, significantly higher capital and utility expenses,
tighter sterility and contamination constraints, and additional heat and mass
transfer complexities.
To illustrate the effects of scale and intensity, Figure 1.3 presents curves
of aggregate capital and utility costs required to transfer oxygen to a fer-
mentor [38]. Per kg of O
2
transferred to living microorganisms, the cost to
own and operate an aerobic fermentor decreases with increasing size and
increasing oxygen uptake rate. Larger fermentors leverage economies of scale
in vessel costs, support equipment costs (air compressor, chiller, etc.) as well
as in the labor associated with reactor operation and monitoring.
6
The oxygen
6
A key difference between Figure 1.3 and
the results in [38] is that one full-time
employee (FTE) has been added to mon-
itor the bioreactor (five shifts at 0.2 FTE
per shift) at a loaded operating expense
of $100k/y. In the aggregate cost, this ex-
pense is negligible at the 200,000 L scale,
but represents ~25% of the total at the
2,000 L scale.
uptake rate (OUR) is the volumetric consumption rate of dissolved O
2
by
cells (mol O
2
/m
3
-h). Attaining a high OUR requires the development of a
robust, metabolically efficient organism, capable of high cell density, high
growth rate, and high productivity. Attaining an equally high oxygen transfer
industrial scale-up perspectives 4
rate (OTR, volumetric dissolution rate of O
2
from sparged gas), especially
in desirably large vessels, requires a significant fermentor design effort to
improve mixing and heat/mass transfer. The OUR and OTR thus stand for
the less concrete metric of process intensity. The concerted biological and
engineering development activities aimed at increasing these quantities are
known as process intensification: getting the most yield from every liter of
the fermentor [39].
Figure 1.3: Specific aggregate capital and
operating cost to transfer O
2
to aerobic
stirred-tank fermentors of varying size.
Many biofuels/chemicals developers found that their microbes were ei-
ther insufficiently robust to scale into economically large fermentors or too
inefficient to operate at high OUR. As a result, developers found themselves
with unacceptably high capital costs when trying to design large plants [40].
Others discovered new problems at scale: heat and mass transfer deficiencies,
uncontrollable contamination, or the inability to keep recombinant organisms
from reverting to their wild type. In the U.S., many scale-up commitments
made by industry and government in the early 2000s were missed or de-
ferred [41]. Even somewhat successful biofuels developers eventually found
their business models obliterated by drastic reductions in the price of oil
(Figure 1.2a), resulting in a series of high-profile failures, bankruptcies, and
acquisitions in the sector [4248].
Cultured meat doesn’t seem to present an easier problem from either a
technical or an economic perspective [49]. To permit process intensification,
metabolic efficiency must be as high as possible.
7
To attract investment, capital
7
In this case, sugars and amino acids to
cellular protein.
costs must be as low as possible. Furthermore, the relatively stable price
of conventional meat (Figure 1.2b) doesn’t present a clear and immediate
economic opportunity in the way that rising oil prices once did for biofuels.
Considering Figure 1.3, a key question seems to be: can an animal cell-
culture process be designed and operated at a scale and intensity where
its consumption as food becomes economically sustainable? Unfortunately,
though several microbial bioprocess technologies have scaled over decades to
extremely large production volumes (e.g., fuel ethanol, baker’s yeast, lysine
for animal feed, wastewater treatment), it is difficult to reconcile even basic
concepts of industrial bioprocess design with known characteristics of animal
cell culture as practiced today. For instance:
Table 1.1: Hydrated diameter, mass, and
doubling time τdfor common cell types.
diam.
mass τd
Mycoplasma 0.4
µm
0.03 pg
6–12 h
Bacteria
1
µm0.5 pg 20 min
Yeast
5
µm60 pg 1–3 h
Fibroblast
14
µm
1500 pg
24–48 h
ÉThe growth rate is slower.
Animal cells proliferate much more slowly than microbial cells (Table 1.1).
Commercial strains of baker’s yeast, for instance, are grown with a doubling
time of about 3.5 hours.
8
After a week of inoculum preparation, a production
8
Cell growth is usually expressed as a rate
µ
having units of g cells/g cells-h (or h
-1
).
A growth rate of
µ
=0.20/h means that 1 g
of cells will multiply into 1.20 g of cells in
1 hour. The doubling time
τD
is the time it
takes for 1 g of cells to double into 2 g. The
two quantities are related by
τD=ln(2)
.
batch of yeast thus lasts ~16 hours [50]. Given a doubling time of 24–
48 hours, a facility that produces an equivalent mass of animal cells would
require 8–16×more bioreactor volume. Production batches would last several
days to a week, following months of inoculum preparation. At food scale, the
total number and volume of installed bioreactors would be staggering.
industrial scale-up perspectives 5
ÉThe bioreactor volumes are smaller.
In a conventionally configured fermentor or bioreactor (gas-sparged and/
or agitated), maximum practical reactor size is often determined by the
cells’ ability to withstand spatial heterogeneities in, e.g., temperature, pH,
or nutrient concentrations [51]. Individual cells in suspension are mixed
throughout the fermentor and are thus subject to varying conditions, which
may stress them. In large fermentors, heterogeneity is typically counteracted
with increased sparging and/or increased agitation. Either action increases
turbulence and bubble-induced shear forces in the fluid, which may damage
animal cells due to their relatively large size and lack of a rigid cell wall [52].
Maximum practical bioreactor size is thus in part determined by the efficacy
of mixing at the limits of shear tolerance. Today, animal cell culture is not
practiced in bioreactors larger than 25 m
3
—significantly smaller than the
200–1,000 m3vessels employed in industrial aerobic fermentation.
ÉThe final cell density is lower.
In high-density fermentation, typical design limits are a sparge rate up to
~2 vvm (standard volumes of gas per volume of liquid per minute) and an
agitation rate up to ~5,000 W/m
3
(agitator power input per volume of liquid).
The equivalent limits for animal cell culture are ~0.01 vvm and ~100 W/m
3
.
These constraints place animal cell culture in a significantly lower oxygen
mass transfer regime than fermentation; upper limits of the O
2
mass transfer
coefficient k
L
aare ~800 h
-1
in fermentation and ~15 h
-1
in cell culture [53].
Due to the animal cells’ lower growth rate, the OTR achievable with such a
low k
L
ais generally adequate to match OUR as cells multiply to low/medium
density [54]. In high-density culture, however, OUR is dominated by the
maintenance respiration rate of existing cells. These design limits thus impose
constraints on the final cell density.
Table 1.2: Market prices of commercial S.
cerevisiae (2018$, dry matter basis)
$/kg Strain/Source
$2.82 Baker’s, BCC Research [55]
$2.61 Brewer’s, BCC [55]
$2.52 Brewer’s, SuperPro [56]
$2.34 Baker’s, Hacking [57]
$2.20 Baker’s, Company 1
The discussion can be paused here to demonstrate the economic impact
of the above constraints on a microbial process where cells are the product:
baker’s yeast (Saccharomyces cerevisiae). While production of mass quantities
of animal cells in large-scale, high-density culture is a novel problem, bakeries,
breweries, and fuel ethanol plants all receive daily shipments of yeast cells.
Commercial yeast is typically produced in large (~200 m
3
) bubble-column
bioreactors at cell density approaching 4×10
9
/mL (70 g/L dry matter) and
extremely high OUR of ~150 mol O
2
/m
3
-h. To avoid ethanol formation, yeast
growth is controlled to a doubling time of 3.5 h [58].
9
As shown in Table 1.2,
9
Much longer than its native doubling time
of 90 minutes.
wholesale baker’s yeast prices are in the range of $2.20–$2.80/kg on a dry
basis, so the actual production cost should be just under $2/kg. This cost
can be reproduced with a first-principles TEA model,
10
as summarized in
10
Further details of the techno-economic
model for yeast and Table 1.3 are given in
Appendix A.
Table 1.3.
If the process described by this model were constrained by the animal
cell culture limits anticipated above,
11
the cost of production would be 7×
11 Constraints:
Doubling time=24 h
Maximum fermentor size=20 m3
Maximum OUR=25 mol O2/m3-h
higher. Such a plant would cost the same to build, but make only 10% as
industrial scale-up perspectives 6
Table 1.3: Analysis summary for standard and constrained yeast processes. (See Appendix A.)
Standard Constrained
(equal CAPEX)
Max. growth rate (h-1 ) 0.20 0.03
Max. OTR (mol O2/m3-h) 150 25
Production fermentors 6×200 m327×20 m3
Final seed fermentors 2×85 m39×19 m3
Cell density (g/L dry) 69 25
Yeast production (kTA) 17.3 1.7
Total CAPEX $69M $70M
Total FTE 24 56
Cost of production, $/kg dry matter
Carbon (molasses) $0.72 $0.89
Nitrogen (ammonia) $0.04 $0.04
Water $0.01 $0.02
Utilities $0.16 $0.23
Labor $0.14 $3.34
Overhead $0.36 $3.63
Annual capital charge $0.47 $4.74
Total COP, $/kg dry $1.89 $12.90
Total COP, $/kg wet $0.57 $3.87
much yeast. For animal cell culture, significant economic penalties are thus
anticipated due to basic engineering constraints of growth rate, bioreactor
size, and oxygen mass transfer. These will tend to push animal cell cultures
into the upper-left corner of Figure 1.3. Unfortunately, there are still more
constraints to consider:
ÉCatabolite inhibition further limits the final cell density.
As mentioned above, animal cells lack a rigid cell wall. An individual muscle
or fat cell in culture is therefore much less capable of excluding or rejecting
unwanted compounds in its environment than a microbial cell.
12
In other
12
That being the job of a different type of
cell in, e.g., the kidneys. Notably, yeast,
which evolved in open environment, can
regulate internal pH independent of the
fermentation broth pH [59].
words, animal cells have osmolality limits. All dissolved species (sugars,
minerals, buffers, waste metabolites, CO
2
, etc.) contribute to osmolality
and their concentrations must be tightly controlled. Waste catabolites like
ammonia and lactate are particularly toxic and inhibit cell growth even at
relatively low concentrations. Indeed, in cell culture for biopharmaceuticals,
accumulation of toxic catabolites is a more frequently encountered limit
than any physical limit of the bioreactor itself. In fed-batch operation, a
catabolite-limited cell density of 1×10
6
–30×10
6
/mL is generally sufficient
for protein production, but it would make the accumulation of bulk cell
mass very challenging. Perfusion technology continuously removes waste
catabolites and other spent media components from the culture to alleviate
inhibition. As a rule, perfusion cultures can achieve higher cell densities than
fed-batch cultures, but the maximum practical bioreactor size is significantly
smaller.
ÉThe availability of high-quality media components is limited.
In fermentation process design, the limited nutrient slate of industrial mi-
crobes is exceptionally handy. Regardless of the organism’s metabolism, the
industrial scale-up perspectives 7
starting materials are the same: a single substrate (usually a sugar) for carbon
and energy, a single inorganic nitrogen source (ammonia or nitrate salt), a
small amount of phosphate, and very small amounts of sulfur and trace metals.
Animal cell-culture media must instead supply a mixture of amino acids to
satisfy the cells’ nitrogen demand. On an atomic nitrogen basis, these are
significantly more expensive than an inorganic nitrogen source, and many
are not currently produced at volumes consistent with a significant scale-up
of animal cell culture.
Furthermore, if the cells to be cultured are stem cells, then a variety of
hormones, cytokines, vitamins, etc. (collectively known as growth factors)
must also be provided to keep them from differentiating as they proliferate.
At the bench scale, these are typically delivered in complex, animal-derived
sera; at food scale, suitable replacements from fermentation or plant-based
sources will be required. As expensive as these compounds are likely to be,
they may not be a significant contributor to cell mass production cost, as their
concentrations in media are extremely small.
ÉThe capital costs of aseptic operation are significant.
At neutral pH and elevated temperature (37
C), an aerated cell-culture
bioreactor is quite welcoming to any stray microbe. Given the relative growth
rates in Table 1.1, a contamination event will very quickly turn an animal
cell culture into a microbial culture, leading to batch loss. The cleanliness of
equipment, environment, and media is therefore critical at every stage of the
cell-culture process. In comparison to a fermentation process, the additional
sterility/asepsis safeguards required by animal cell culture will have a strong
effect on the cost of equipment and facility: extra steam piping for point
sterilization, extreme automation to avoid contamination by operators, and
containment considerations for biosafety. These measures will reduce the
economies of scale typically expected as a function of vessel volume, and
may limit the ultimate bioreactor size as well, given that current designs
of fermentors larger than ~200 m
3
are not practicably sterilized to a level
suitable for animal cell culture [60].
ÉA significant metabolic engineering is required.
A cell line suitable for an economic bulk-growth process would have several
traits that are generally not characteristic of the wild-type cells obtained from
a live-animal biopsy (Figure 1.1). Primary cells, which are fully differentiated
to their final tissue type (e.g., muscle or fat), can only be propagated for ~50
generations before proliferation ceases—the so-called Hayflick limit. Within
this limit, several tons of cell mass could, in principle, be grown from the
primary cells in a tiny biopsy. In practice, scaling up mortal cell lines to
industrial volumes will be extremely challenging, as phenotypic variations in
every new biopsy will demand process re-development and re-qualification.
For repeatability at scale, immortal (or immortalized) cell lines will be re-
quired, e.g., adult (partially differentiated) stem cells from tissue, embryonic
industrial scale-up perspectives 8
stem cells (ESCs) from a recently fertilized embryo, or induced pluripotent
stem cells (iPSCs) produced by genetic reprogramming of adult cells [61].
Stem cells, however, are notoriously difficult to culture without differenti-
ating [62]. Furthermore, all normal animal cells are generally anchorage-
dependent, meaning that they prefer to adhere to something during growth.
In animal tissue, cells adhere both to each other and to a complex extracellular
matrix, which is vascularized to ensure that each cell receives nutrients and
oxygen via the blood stream. In adherent culture for upstream biopharmaceu-
ticals, cells adhere to the bottom of a T-flask or the inside of a roller bottle.
13
13Scale-up law: buy another roller bottle!
To mimic a suspension culture (albeit one with even stricter shear limitations),
some cell lines are adapted for culture on microcarriers
14
Primary cells can
14
Microscopic beads of (e.g.) collagen or
polymer.
also be “transformed” in the lab, a process that in many cases produces an
immortalized, anchorage-independent cell line that may be grown in free
suspension.
Figure 1.4: Global prescription drug rev-
enue, 2018 [63].
ÉThe value propositions are completely different.
Many of the process design challenges and economic disadvantages high-
lighted above for animal cell culture are only tolerated because the products
are extremely valuable. These products include glycosylated protein thera-
peutics,15 primarily produced in recombinant Chinese hamster ovary (CHO)
15
Protein molecules with a folded structure
influenced by attached sugar molecules.
Glycosylation of a mammalian protein
must be done by a mammalian cell. While
a microbial cell could perhaps be engi-
neered to make a protein with the same
amino acid sequence, it would not be gly-
cosylated and thus not an effective thera-
peutic.
cells. Figure 1.4 presents a breakdown of global prescription drug revenue
in 2018 [63]. Recombinant glycoproteins belong to a class of drugs called
biopharmaceuticals or biologics,
16
and most can also be further classified as
16
This classification includes products from
microbial fermentation as well as some
made in whole animals and plants.
monoclonal antibodies, or mAbs. In 2018, biologics accounted for about 25%
of global prescription drug revenue, and mAbs made up about half of that
share. Of the 80 approved mAb products represented in Figure 1.4, adali-
mumab (Humira) alone accounted for 20% of revenue: $20B in 2018 [63].
In the U.S., Humira (3 months of biweekly doses of 40 mg) was prescribed
4.2M times in 2016 [64,65]. It can thus be approximated that the U.S. patient
base for Humira is about 1M individuals, and its annual U.S. production
volume (as a pure ingredient) is 1,100 kg—enough to fill the back of one
pickup truck.
17
In 2017, U.S. sales of Humira were $12.4B [66], i.e., the
17
For comparison, the U.S. ethanol in-
dustry produced 16B gallons that year—
enough to fill 2M tanker trucks.
selling price was >$11M/kg.
These figures do not say much about the putative costs of growing animal
cells. Petrides [56,67,68] presents a techno-economic analysis of a generic
mAb facility that produces ~1,500 kg/y of mAb from CHO cell culture in
20 m
3
bioreactors at an estimated unit production cost of $84,000/kg, divided
roughly 72% upstream (cell culture) and 28% downstream (recovery and
purification of the mAb). In contrast to most fermentation processes [57],
the largest upstream cost is not feedstock (i.e., cell-culture media). Rather,
it is facility and labor: a $110M clean room and ~130 workers. The largest
downstream cost is consumables: resins, filters, etc. used in product purifica-
tion. Normalizing this analysis for the 42,000 kg/y (wet) of co-produced CHO
cell mass would result in $2,200/kg of CHO cells. The comparison is odious;
a mAb process of course is not optimized for a high yield of cell mass, which
analysis approach: powers of ten 9
is a waste stream in the process and a consumer of carbon and nitrogen that
could otherwise be directed to product.18
18
In almost all existing manufacturing pro-
cesses using animal cells, one would prefer
to minimize the cell mass. In nascent appli-
cations where this is not true, e.g., single-
patient cell therapies including CAR-T, the
scales are tiny, with bioreactors the size of
a deck of cards, or a can of soda [69].
To summarize, the state of the art in large-scale animal cell culture is in
addressing very specific problems (production of recombinant glycoprotein
therapeutics) by making very small amounts of something (few hundred to
~2,000 kg/y) that improves the lives of a very small number of people (few
thousand to ~2M) and sells for a very high price (e.g., $11M/kg) at an arbi-
trarily high margin [70].
19
It is not, it would seem, a likely platform for making
19
Perhaps also worth noting from Fig-
ure 1.4 that 75% of prescription drugs
revenues derive from non-biologics: small
molecules synthesized without cells. Even
in protein therapeutics, the next (albeit
controversial) technology on the horizon
appears to be cell-free expression [71].
low-value, commodity-scale products like food. Looking to blockbuster
20
mAb
20A drug with >$1B in annual sales.
processes for scale-up guidance reveals that conventional animal cell-culture
processes are carried out on a vastly smaller scale than food production. In
addition, they have not necessarily been optimized for the same economic
levers as industrial fermentation, e.g., yield of cell mass or even media cost.
Instead, they have individually been optimized for something else which is
process- and product-specific. The scale-up laws and economics of animal cell
mass production thus remain uncertain.
1.3 Analysis approach: powers of ten
At time of writing (Fall 2020), the production volume of edible cultured
animal cells is unknown but small—probably on the order of 1–10 kg/y of
material generated as demonstration product and in the course of R&D. The
current production volume of conventional meat is estimated at 3.2×10
11
kg/y
(320,000 kTA, kilotonne per annum) [72]. Ultimate aspirations for cultured-
meat products would thus appear to be on the order of 10
11
kg/y, or billions of
people consuming tens of kg/y [4]. With techno-economic analysis, we gaze
into this abyss of ten orders of magnitude. As noted above with the eleven-
dollar burger, to conceptualize and mentally process the scales involved, one
may be tempted to invoke some form of Moore’s law. Indeed, depending on
the metric (processing speed/power, consumer price, etc.), it can be argued
that certain aspects of computing have progressed by about ten orders of
magnitude since the days of Moore [73,74].
21
Most of this progress can
21
And it only took 60 years. To fit this
many powers of ten into a time scale that
meets contemporary investor expectations,
some would suggest that even more accel-
erationist “laws” are in play for cultured
meat [75].
be explained in the context of the original observation—from a nominal
transistor size of ~10
µm
in 1970 to ~10 nm today, there were at least six
orders of magnitude of improvement to be made in the number of 2-D devices
crammed into a square centimeter of silicon [76]. The remainder is a result
of concomitant advances in chip design, materials, process development,
software, etc.
Unfortunately, similar progress cannot be expected of biological systems,
whether in vivo or in vitro. The chemical reactions occurring inside a living
cell proceed with the usual thermodynamic efficiency of 30–80% [77]. If
an organism lives at all, it does not do so orders of magnitude away from
its physical limits. Furthermore, in contrast to the semiconductor industry,
momentous advances in manufacturing are less expected in the process indus-
tries. The basic phenomena of fluid flow, separations, mass transfer, reaction,
analysis approach: powers of ten 10
and the process equipment these take place in likewise operate with the usual
thermodynamic efficiency of 30–80%. While generally accepted economies
of scale in the process industries hold that, e.g., equipment costs scale sub-
linearly with capacity [78],
22
or that the unit price of a commodity precursor
22
Cost2
Cost1
=Capacity2
Capacity1a
;a0.6
chemical scales sub-linearly with order quantity [79],
23
these effects do not
23
Unit price2
Unit Price1
=Qty1
Qty2a
;a0.6
hold within them multiple orders of magnitude in manufacturing cost reduc-
tion. Nor do they necessarily apply in the case of biotechnology, where the
process equipment in question is much smaller and more specialized than
refinery/chemical equipment, and where the precursor chemicals (e.g., sugars,
amino acids, growth factors) are only produced in limited quantities.
Consider, for instance, Figure 1.3: a 10×increase in fermentor volume
does not result in a 10×reduction in the cost of O
2
transfer. A 10×increase
in OUR can result in such a reduction, but this quantity is not infinitely valued.
In fermentation, 200 mol O
2
/m
3
-h is about as high as it gets; in animal cell
culture, a practical limit is <50 mol O
2
/m
3
-h. Thus, unlike the future cost
to make a solid-state transistor looking forward from 1965, the absolute
minimum cost to make a bioproduct (fuel, chemical, drug, or meat) is not
unknowably small. Rather, it can be straightforwardly examined with techno-
economic analysis. When performed responsibly, estimates from TEA can
claim to be accurate to within 50% [80]. In other words, a projection might
be off by a factor of two—not by a factor of ten.
Critically, the above claim is valid only in the context of the TEA’s charac-
teristic assumptions. Projections across ten orders of magnitude must carry
some uncertainty, however, and care must be taken to avoid unreasonable
assumptions and magical thinking. Technical due diligence, a related activity
to TEA, is the art of interrogating such projections to distinguish between
those that are challenging but achievable and those that are misleading or
provably unphysical. For instance, while an “eleven-dollar burger” certainly
sounds like a reasonable value for one’s money, smart shoppers may note
that an $11 hamburger at the factory easily becomes a $30 hamburger at
the supermarket and a $100+ hamburger served at a restaurant. Absent
other market pressures, one would not expect such an expensive product to
measurably displace the consumption of conventional meat. Due diligence
of this projection would raise additional questions about its capital equip-
ment and media cost assumptions, facility and overhead costs, the contents
of moisture and other fillers in the product, and the degrees to which the
laws of biology and physics were upheld in its generation. In this analyst’s
related experience with biofuels, some commonly observed deficiencies in
TEA (public and private) included:
Yield projections in excess of biological and thermodynamic limits.
Overestimation of economies of scale in equipment and plant size.
Unrealistic expectations of supply-chain expansions at scale.
Arbitrarily high values assigned to hypothetical or unproven co-products.
A reliance on government intervention to enforce competitiveness.
analysis approach: powers of ten 11
All of these are still in play for cultured meat. Others noted during the
preparation and review of the present analysis include: media cost projections
inconsistent with their required quality and putative demand, media usage
projections inconsistent with cellular growth stoichiometry, and a tendency
to willfully underestimate or ignore outright the likely capital costs of the
ultimate production facility.
24
The present analysis therefore takes a due-
24
Some of my due-diligence colleagues
and I have lately (re-)observed this trend
among bioeconomy developers and in-
vestors. The reasoning usually follows a
line of “CAPEX only matters for the first
plant; all subsequent plants will be fi-
nanced at a low cost of capital.” Though
not technically incorrect, such treatment
from lenders is, more accurately, only en-
joyed after the first successful plant. This
need to reconcile a sense of urgency with a
reluctance to be “first” was an exceedingly
common source of friction in the days of
venture-backed biofuels startups [49].
diligence approach from the beginning, to provide a transparent techno-
economic projection of an animal cell culture process designed for bulk growth
of cell mass at commodity scale.
Section 2explores technical aspects of cellular growth stoichiometry and
metabolism. Basic bioreactor design rules are used to establish maximum cell
density as a function of bioreactor size. Sterility issues are also discussed.
Section 3explores economic aspects of capital and operating costs. General
cost trends for media components and sterile bioprocessing equipment are
developed. Section 4develops production cost estimates and sensitivities for
conceptual fed-batch and perfusion processes. To simplify the problem and
the conclusions of the analysis, some characteristics of the model processes
are assumed a priori. These aspects do not (wittingly) reflect the designs
of any existing developer,
25
but will help to identify the general scale-up
25
In preparing this report, I had limited
interactions with cultured-meat develop-
ers, and I am not under a confidentiality
agreement with any of them.
constraints expected for any cell-culture technology:
A mammalian (warm-blooded) cell line is considered for thermodynamic
purposes.
Conventional stainless-steel construction is assumed for the facility.
Suspension culture is favored.
The only inputs to the culture are water, air/O
2
, glucose, amino acids,
and some key growth factors.26
26
Buffers and low-cost mineral salt compo-
nents are not included in the media-cost
model.
The only revenue output from the culture is unstructured animal cells,
suitable as a starting material for downstream processing to food. Rev-
enue from unspecified co-products (including intellectual property) is
not considered.
Except where noted (mainly Section 2.2), cell mass is reported on a
wet-matter basis, assuming 70% moisture.
Certain aspects of the analysis must be examined within the context of
an entire industry. In particular, it will be demonstrated that cultured meat
scale-up is contingent on concomitant scale-up of other bioproducts (e.g.,
amino acids and growth factors) and some global scale must be assumed to
assess the demand on those industries. For discussion purposes, a threshold
for a modest but measurable displacement of conventional meat by cultured
meat is taken as 100 kTA of wet animal cell mass, i.e., ten million people
consuming 10 kg/y each. In round numbers, 100 kTA is roughly equivalent to
the current production volume of ascendant plant-based meat replacements,
which have wide recognition and global distribution.
27
Further cost reductions
27
Products from, e.g., Beyond Meat and
Impossible Foods.
are likely at larger scale, of course, and these will be examined with sensitivity
analyses. However, 100 kTA of animal cell mass shall reflect a waypoint in the
analysis approach: powers of ten 12
development and adoption of cultured meat, one that should be squarely be-
yond the “valley of death” associated with new bioproduct development [26].
To assert an affordability threshold at this scale, this analyst submits a tar-
get of ~$25/kg of wet animal cell matter produced in a bulk growth step.
To reach a market of ten million consumers, it must be assumed that any
extravagant price premiums associated with product novelty have expired,
and that cultured meat has at least attained the price-acceptance status of a
“sometimes” food. After further processing, packaging, distribution, and profit,
unstructured products made 100% from bulk cell mass at $25/kg might be
expected to reach a minimum of $50/kg ($23/lb) at the supermarket—the
price of a premium cut of meat, paid instead for a mincemeat- or nugget-style
product. Above this cost, conventional meat displacement may arguably be
measurable but increasingly less significant.
2
Technical aspects
2.1 Model cell characteristics
Different animal cell types have been proposed for cultured meat production,
including embryonic or pluripotent stem cells (undifferentiated), adult or
mesenchymal stem cells (partially differentiated), and primary cells (fully
differentiated to their final tissue type) [61]. Each of these would have char-
acteristic growth phases: a proliferation phase in which the cells multiply
in number; one or more differentiation phases; and possibly a hypertrophy
phase, in which the cells (as muscle tissue) accumulate mass without nec-
essarily increasing in number. Each growth phase might further require a
specific media composition, different growth factors, and a different bioreac-
tor design. These details are presently unknown, or at least not scientifically
demonstrated in the public sphere.
Much more is known about mammalian cell lines used in biopharma-
ceuticals manufacturing, most of which derive from CHO (Chinese hamster
ovary) cells, as discussed in Section 1.2 [81]. CHO cell lines are immortal,
non-cancerous, and morphologically stable [82,83]. They can be grown
in adherent culture or in high-density suspension culture. They can also
withstand genetic manipulation with relatively good clonal stability [83],
which facilitates batch predictability. CHO cells are not stem cells and require
only a limited number of growth factors, making it possible (though still
challenging) to design cost-optimized, serum-free media [84]. By degrees,
CHO cultures thus overcome some of the process design issues anticipated in
Section 1.2. CHO cells are not food, of course, nor is their use as such being
proposed. However, this analysis draws on a large body of CHO research to
make technical assumptions about mammalian cellular metabolism, growth
inhibition, bioreactor design, and other aspects.
To generalize bulk cell culture for modeling purposes, this analysis con-
siders an abstract 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.
28
Noting that suspension culture is
28
And larger than CHO cells, which are
1,000–2,000 pg wet [85].
likely to be the lowest-cost option for bulk cell growth,
29
it is further assumed
29
To be discussed from a bioreactor design
perspective in Section 2.3.
13
model cell characteristics 14
Table 2.1: Constituent composition for animal cell mass (dry CHON basis).
C-formula HfGfWt% mol/mol
kJ/mol
Lipid CH2O0.13 [Palmitate] 54.0 17.8 15% 0.205
Carbohydrate CH2O205 147 10% 0.073
RNA/DNA CH1.13O0.74N0.39 [89]119 72.6 5% 0.036
Protein CH1.57O0.31 N0.28 [90]62.2 21.7 70% 0.686
Overall (DCMa) CH1.68O0.34N0.21 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
µm
. Cell growth proceeds in
the usual way with a maximum growth rate
µmax
=0.029/h, equivalent to a
doubling time of 24 h.
30
On a bulk-mass basis, if a culture is gaining mass
30
See Note 8for a description of “usual”
cell growth.
then it must be consuming mass (i.e., nutrients and O
2
) at a rate consistent
with some growth stoichiometry.
31
If the culture is alive but not gaining mass,
31To be discussed in Section 2.2.
then it must still be consuming nutrients for maintenance.
A CHON formula for animal dry cell mass (DCM
a
) of CH
1.68
O
0.34
N
0.21
is de-
rived in Table 2.1 from an average composition of a mammalian cell [86] and
representative CHON formulas of constituent macromolecules.
32
Enthalpies
32
For purposes of this analysis, sulfur, phos-
phorous, and metals are ignored. Addi-
tionally, the typically cited 5–10% weight
fraction of intracellular small metabolites
is assumed to have a composition reflective
of the macromolecular composition and is
thus normalized out.
of formation (
H
f
) for the constituent macromolecules and cell mass were
estimated from the C-formulas and the correlation of Burnham [87]. En-
tropies of formation (
S
f
) were estimated with the correlation of Battley [88].
From these values, Gibbs free energies of formation (
G
f
) were estimated at
a reference temperature of 298 K.33
33Gf=HfTSf
Note 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 10
6
/mL) is a commonly reported quantity.
34
Errors in techno-
34
As 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
η
of a suspension as a function of the volume
fraction φoccupied by particles.35
35
Here,
η0
is the native liquid viscosity
(~0.8 cp for cell-culture media at 37
C)
and
φmax
=0.65, an appropriate packing
limit for soft spheres [91].
η/η0=1φ
φmax 2.5φmax
(2.1)
Allowing for additional viscosity contributions from growth-factor and extra-
cellular proteins, a limiting volume fraction of cells can be taken as
φ
~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
stoichiometry of animal cell growth 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
φ
=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 40×10
6
/mL for a cell size approaching 4,500 pg [13] is in fact much closer
to the viscosity limit than a “challenging” assumption of 128×10
6
/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%
Figure 2.1: Phase-contrast microscopy of
CHO cell suspensions at 10–30% volume
fraction [91].
Table 2.2: Attainable number and mass density at volume fraction
φ
=0.25 for various cell sizes.
Specific O2uptake rates predicted by Reaction 2.9 are also shown.
Wet mass Diam. Max. density Specific OUR
pg/cell µm106/mL g/L wet pmol O2/cell-h mg O2/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
2.2 Stoichiometry of animal cell growth
The stoichiometry of life is the sum of anabolism, growth-associated catabolism,
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 organic nitrogen 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.
stoichiometry of animal cell growth 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 O
2
, CO
2
, pH, temperature, etc.) could be controlled
dynamically and independently in cell culture, the options could be eliminated
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.
ÉAnabolism
The anabolic reaction for 1 mole of DCM
a
(Table 2.1) can be divided into
subreactions for the constituent components.
36
The lipid fraction, which
36
Abbreviations, 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
37
Cellular 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/mol G=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/mol G=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
38
Note that the apparent CO
2
requirement
in Reaction 2.4 is more than satisfied by
the CO2generated 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/mol G=1.5 kJ/mol (2.4)
stoichiometry of animal cell growth 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/mol G=9.9 kJ/mol (2.5)
For cell mass growth from individual amino acids, the following anabolic
reaction (the superposition of Reactions 2.22.5) 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/mol G=2.8 kJ/mol (2.6)
ÉWild-type catabolism
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.
39
Guan and
39
Decades of such experiments for indus-
trial microbes have generated an array
of engineering correlations describing fer-
mentation energetics for first-principles
process design [88,9698]. 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-
γ
) along with lactate (Lac), CO
2
, and NH
3
[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/mol G=700 kJ/mol (2.7)
Reaction 2.7 has a few notable aspects. First, its
H
r
and
G
r
are 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
stoichiometry of animal cell growth 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.
40
For example, as written, it
40
These 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
H
r
of 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 P
M
can be scaled to hydrated cell mass with a 3/4 exponent:41
41
P
M
can 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=0.148M0.75
c(PMin pW, Mcin pg)(2.8)
In West’s relation, cells with wet mass 3,000 pg have a P
M
of 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
µ
=0.029/h and combining the anabolic and catabolic contribu-
tions into a single reaction in mol/mol DCMa-h:42
42
Note 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/mol G=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) that can be synthesized from other available amino acids if not provided
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,
43
Figure 2.2 compares their relative macronutrient profiles. With
43
High 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.
stoichiometry of animal cell growth 19
Figure 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 O
2
/cell-h [106]. At a growth rate of
µ
=0.029/h, the SOUR pre-
dicted by Reaction 2.9 is in good agreement with this value (0.30 pmol O
2
/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.
ÉEnhanced catabolism
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 O
2
for respiration is provided,
and to catabolize amino acids for energy even when ample glucose is provided.
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 likely
44
that an assumption of high
44
And perhaps thermodynamically intu-
itive.
metabolic efficiency is inconsistent with an assumption of high growth rate.
stoichiometry of animal cell growth 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-
line characterization and engineering. These include: selection for phenotypes
with lactate reuptake capability;
45
genetic modification to express a glutamine
45Aerobic catabolism of Lac.
synthetase enzyme;
46
and feedback control of glucose concentration and
46
Intracellular synthesis of Gln from Glu
and NH3.
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
47
The 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/mol G=2, 271 kJ/mol (2.10)
For 60 pW/cell, this catabolism proceeds at 0.0024 mol/mol DCM
a
-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/mol G=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 DCM
a
by about 60% each over Reaction 2.9 (see Table 2.3). Even if full
respiration were assumed, eliminating Lac and NH
3
entirely, the additional
improvement is marginal. In either case, the relative O
2
uptake and CO
2
generation rates are higher with the more efficient metabolism. These have
implications for bioreactor design, to be discussed in Section 2.3.
Table 2.3: Stoichiometric uptake (nega-
tive) or generation (positive) per mole of
DCM
a
for 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 0.46
ÉComplex amino acid sources
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, CO
2
, and fossil
fuel.48 These fundamental sources, and the plants produced from them, are 48Former sunlight and CO2.
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.
stoichiometry of animal cell growth 21
Natural
gas
Natural
gas
Carbohydrate
crop
Protein
crop
Hydrolysate
Refined sugar
MillingMilling
Power plantPower plant
Ammonia plantAmmonia plant
Oilseed millOilseed mill
Growth factors
Amino acids
HydrolysisHydrolysis Cell cultureCell culture
FermentationFermentation
Meal
Ferm.
nutrient
Fertilizer
Sun + CO2
+ refining
+ refining
Cell
mass
Figure 2.3: Material flows upstream of the cell-culture facility, starting from sunlight, CO
2
, and
natural gas.
Figure 2.4 compares the amino-acid profile of the protein synthesis reaction
(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,
49
all EAA requirements could be met except for glutamine
49To match on threonine.
(which must be fed separately in any case) and about 75% of tyrosine.
50
With
50
Soybeans 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 (C2.63H4.86 O1.75N0.60)
H=197 kJ/mol G=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 (C2.63H4.86 O1.75N0.60)
H=197 kJ/mol G=204 kJ/mol (2.13)
bioreactor design principles and limitations 22
Figure 2.4: Amino-acid profiles of cellular protein (Reaction 2.5) and U.S. soybean meal.
2.3 Bioreactor 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 m
3
stirred-tank bioreactor (STR) as
the final production vessel, operating in fed-batch mode with a final cell den-
sity of 128×10
6
/mL.
51
Individually, this bioreactor volume and cell density
51
At 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,
typical fed-batch cell densities are rather closer to 10×10
6
–30×10
6
/mL at any
volume, which is sufficient for protein production at modern titers [110]. Cell
densities on the order of 100×10
6
/mL are more consistent with high-density
perfusion cultures.
Jacket
Jacket
T
D=T/3
Sparger
H = 2 T
0.8 H
Figure 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 O
2
into solution and strip CO
2
out in all large bioreactor designs
(>~1 m
3
). 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 u
s
(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/m
3
) or per unit of liquid mass (
¯
"
=P/
ρ
V, in W/kg.)
bioreactor design principles and limitations 23
In sparged bioreactors, cells in suspension tend to attach to a rising bubble’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,
52
while that from bursting and
52
For 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
53
A common feature of record-high-
density animal cell cultures is that they
are not sparged at all, with O
2
instead 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 m
3
, though much smaller reactors of 1–2 m
3
are more
common. At larger scale, O
2
depletion in the ungassed downcomer can
become prohibitive [114].
54
Gently sparged STRs are thus preferred. Physical
54
Li et al. [115] offered a CFD model of
a hypothetical 300 m
3
airlift reactor for
CHO cell culture. Their simulations in-
dicated 46% (3.2 mg/L) dissolved O
2
at
the top of the sparged column, about half
of which was consumed by cells during
a 20-second trip through the downcomer.
Upon review, however, I find that the SOUR
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
references [106]. With this correction, the
simulations would instead have concluded
that available O
2
was depleted and that
the cells were stressed at the downcomer
exit.
constraints of the STR that limit the ultimate cell density will be discussed
below, using bioreactor design concepts.
ÉO2mass transfer
Industrial fermentor scale-up is often approached as a constant O
2
mass
transfer problem [38,117]. Here, the volumetric OTR is modeled as the
product of a mass transfer coefficient k
L
aand a concentration driving force,
which is the deviation of the dissolved oxygen concentration
CO2
(also known
as DO) from its saturated concentration
C
O2
. The saturated concentration is
given by Henry’s law:
C
O2=yO2P×HO2(2.14)
If the fermentor (or bioreactor) is sparged with air, y
O2
at the bottom is 21%.
At the top, y
O2
is determined with an O
2
mass balance. In a very tall vessel,
the local pressure Pmay be significantly higher at the bottom than at the top.
The average driving force is thus usually expressed as a log-mean difference
over top and bottom:
OTR =kLaC
O2
CO2btm
C
O2
CO2top
ln C
O2CO2btm
C
O2CO2top (2.15)
To determine k
L
a, the correlation of Xing et al. [106] was developed for
CHO cell-culture media at 37 C:
kLa[s1] = 0.075(P/V)0.47(us)0.8 (2.16)
As mentioned in Section 1.2, typical limits on sparging and agitation are much
lower for animal cell culture than they are for high-density fermentation. STR
bioreactor design principles and limitations 24
design rules for cell culture recommend scale-up at a constant but low vvm, to
ensure constant CO
2
stripping when the respiratory quotient is close to 1 [111].
Guidance on maximum sparge rate is usually <0.1 vvm [54,118], though
the O
2
demand of most low- to medium-density cell cultures can usually
be satisfied with much less.
55
For agitation, historical guidance has been to
55
0.01 vvm is common [53]. Additionally,
copious surfactants for foaming and shear
control are typically recommended to mini-
mize cell damage in vigorously sparged cul-
tures, e.g., Pluronic F-68 at >0.5 g/L [111].
Though not especially toxic [119], F-68 is
probably not very tasty, and vigorous sparg-
ing should be avoided.
limit the impeller rotation to a tip speed of <2 m/s. The theory behind this
guidance holds that a low tip speed avoids bubble dispersion (i.e., slicing),
which could potentially create bubbles small enough to collapse in the liquid
phase, creating locally high shear [120].
However, neither tip speed nor vvm has a constant hydrodynamic effect
across reactor sizes. For the present analysis, these design limits are recast into
a more constant frame that directly impacts O
2
mass transfer as determined
by Equation 2.16. Sparging is limited to a superficial velocity of 0.006 m/s at
the top of the vessel.
56
For the agitation limit, more modern analyses prefer
56
This sparge rate is equivalent to 0.1 vvm
in a 20 m
3
bioreactor with the geometry
in Figure 2.5, sparged with air and having
5 psig back pressure.
the explanation that any cell damage caused by the impeller is more likely a
result of turbulent eddies on the length scale of a single cell (~20
µm
) [121].
In Kolmogorov’s theory, the turbulent eddy length
λK
is a function of turbulent
energy dissipation
"T
, with the smallest eddies occurring very close to the
impeller at "T,max:
λK=ν3/"T,max1/4(2.17)
where
ν
=
η
/
ρ
is the kinematic viscosity of the medium fluid.
57
For impellers
57
Not the bulk suspension viscosity [122].
with relative diameter D=T/3, Nienow recommends "T,max=50 ¯
"T[123].58
58
Power input Pcan also be expressed as a
function of the impeller power number N
p
and its rotational speed N(rpm) [124]:
P=2NpN3ρLD5
s
With this relation, it can be shown that an
eddy length of 20
µm
is indeed reached at
a tip speed of ~2 m/s in a 20 m3bioreac-
tor.
With sparging and agitation both at their maximum recommended level,
a maximum attainable mass transfer coefficient can be estimated from Equa-
tion 2.16, and a maximum OTR from Equation 2.15. At the top of the bioreac-
tor, the DO is taken to be 1.4 mg/L (20% atmospheric saturation) for animal
cells. The DO at the bottom is taken to be this value times the bottom-top
pressure ratio (P
top
=5 psig and P
btm
is a function of liquid height).
59
The
59
In a well-mixed STR, the DO gradient
is probably less severe than this. For the
vessel sizes considered here, however, any
errors introduced by this assumption are
small (<0.5%).
cell density is thus limited to the point where the culture’s OUR (based on
catabolic O2demand) is equal to the bioreactor’s maximum OTR.
ÉCO2mass transfer
Respiring cells release CO
2
, which lowers the broth pH. High CO
2
levels
require counteraction with high concentrations of buffering agents, which
may in turn cause osmolality constraints [111]. CO
2
mass transfer from the
liquid phase to passing bubbles follows a relation much like Equation 2.15,
and the CO
2
transfer rate (CTR) is approximately equal to the OTR. Since
the respiratory quotient of growth is approximately 1, it follows that CO
2
is stripped from the liquid phase at a rate equal to its generation, and its
liquid concentration is a function of OTR, which is in turn a function of the
bioreactor sparge rate.
This liquid concentration is typically measured in terms of pCO
2
, or the
CO
2
partial pressure in equilibrium with the liquid phase.
60
In CHO culture, it
60
pCO
2
=y
CO2
P
back
, i.e., the bioreactor
back pressure times the mole fraction of
CO
2
in the outlet gas, which is computed
from a mass balance.
has been shown that productivity is maximized when pCO
2
is maintained in
bioreactor design principles and limitations 25
the range of 40–100 mbar; above 130 mbar, growth inhibition is noted [125].
If the bioreactor is well mixed, it can be assumed that gradients in CO
2
liquid concentration are small. With sparging fixed at u
s
=0.006 m/s, the cell
density must thus be limited such that the CO
2
generation rate does not cause
pCO2>100 mbar.
A corollary to the above discussion: Growth inhibition or cell density limits
caused by high pCO
2
cannot easily be mitigated with metabolic efficiency
improvements. Consider the earlier catabolic parameters of Lac/Glc and
Gln/Glc. No matter how these are specified, the respiratory quotient (CO
2
/
O
2
) of the overall growth reaction will remain ~1 and the CO
2
stripping rate
will remain roughly equal to the O
2
transfer rate. The only way to circumvent
a pCO
2
limit in a sparged bioreactor is to sparge harder, possibly to the point
of cell death. This limitation may preclude the scale-up of animal cell culture
into extremely large bioreactors.
ÉHeat transfer
As observed in Reactions 2.9 and 2.11, animal cell growth is only slightly
exothermic. At low cell density and/or in a small bioreactor having a high
surface area/volume ratio, it is common for heat to be lost to the surroundings
faster than it is generated in the culture, such that the culture requires heating
rather than cooling to maintain a constant 37
C. This requirement stands
in rather stark contrast to high-OUR microbial fermentation, which can have
tremendous heat removal loads that may limit the ultimate fermentor size
on scale-up when, e.g., a cooling jacket no longer provides enough heat
transfer area and aseptic requirements preclude the use of internal coils or
external circulation through a heat exchanger [126]. For animal cells in low-
OUR suspension culture, heat transfer is not anticipated to pose a significant
problem in 200 m3bioreactors.
ÉMixing
In the STR, a mixing time can be estimated with Equation 2.18, which is
based on agitator power dissipation and does not require many details of the
bioreactor or of the fluid being stirred [121]:
tm6T2/3(P/VρL)1/3(D/T)1/3(HL/T)2.5 (2.18)
Here, H
L
is the instantaneous liquid height. A good rule of thumb is that
the mixing time should be less than 1/k
L
a[127]. At longer mixing times,
tm>1/kLawould indicate either that dissolved O2is not being quickly trans-
ported away from the bubble (which reduces the effective concentration
driving force), or that concentration gradients created by respiring cells may
arise faster than they can be canceled out by stirring.
ÉWaste catabolite inhibition
In fed-batch operation, which is common in large-scale cell culture, a bioreac-
tor is inoculated into fresh medium at less than full volume (Figure 2.6a). As
bioreactor design principles and limitations 26
the culture grows and the initial medium is depleted, concentrated nutrients
are added to replenish. The liquid volume in the bioreactor increases until it
reaches a maximum working volume and the batch is harvested. At the start
of a fed batch, cell growth may proceed at the maximum rate
µmax
. As the
increasing cell density drives the bioreactor to one or more limits, growth may
slow. In fed-batch processes for upstream biopharmaceuticals production, the
accumulation of toxic and growth-inhibiting waste metabolites like ammonia
and lactate is a more frequently encountered limit than the physical limits
discussed so far [128]. In many such processes, growth inhibition late in the
batch is not necessarily a concern if the limiting cell density is sufficient for
protein accumulation
61
and this limit and corresponding low growth rate can
61
1×10
6
–30×10
6
cell/mL, depending on
titer [110]
be maintained without cell stress or death. However, for bulk cell production
at typical animal-cell growth rates, it would be economically unfavorable to
run a fed batch very long after
µ
drops significantly below
µmax
. The fed-
batch start/end conditions must therefore be set carefully such that
µmax
is
maintained throughout.62
62
An example of this is given in Ap-
pendix A, in the discussion surrounding
Figure A.3.
Sparge
Sweep
Cell bleed
Vent
Perfusate
Cell retention
device
Sparge
Makeup
media
Sweep
Harvest (t=tEnd)
Vent
Inoculum (t=0)
Fresh media (t=0)
Final volume (t=tEnd)
(a)
(b)
Makeup
media
Figure 2.6: Bioreactor operating modes.
(a) Fed batch. (b) Perfusion.
The inhibiting concentrations of ammonia and lactate vary with cell line,
as do the rates at which cells produce these. A range of 2–10 mmol/L NH
3
has been reported for mammalian cells [90], while lactate inhibition levels
are generally an order of magnitude higher. For analysis purposes, consider
the limits of 5 mmol/L NH
3
and 50 mmol/L lactate. Figure 2.7a presents a
simulation of a fed batch in a 20 m
3
STR where the batch end conditions
have been set to a final liquid volume of 16 m
3
(80% working volume)
after 6 doublings of the initial cell mass (as suggested in [4]) and a limiting
concentration of either NH
3
or lactate (whichever is reached first). The culture
in Figure 2.7a follows Reaction 2.9.
63
To meet these end conditions, the batch
63
Additional details of the fed-batch sim-
ulation procedure will be given in Sec-
tion 4.1.
must be started very close to full (76% WV) and at a very low density of
0.03×10
6
/mL (0.09 g/L). This is well below the general recommendation
for starting cell density, which is ~0.1×10
6
/mL [129]. Below this density,
cultures of many animal cell lines will go into a lag phase (i.e., the initial
growth rate will be very low) or die entirely. After 6 doublings, the final cell
density at 16 m3is only 1.8×106/mL (5.4 g/L).
To avoid lag, the recommended split in animal-cell propagation is a mul-
tiple of 5–10×(2–3 doublings) per stage [129]. Figure 2.7a (solid lines)
shows a shorter simulation limited to 2 doublings. Here, the batch can be
started at a more reasonable cell density of 0.6×10
6
/mL but the final density
is still 2.3×10
6
/mL (7.0 g/L). Neither simulation yields more than 100 kg
of wet cell mass for the effort. In fact, there is no practical way to reach an
economically high cell density in fed-batch operation with a metabolism as
inefficient as Reaction 2.9. At any appreciable starting density, the ammonia
inhibition limit would be reached in a matter of hours.
As discussed in Section 2.2, the wild-type Reaction 2.9 (Lac/Glc=1.77 and
Gln/Glc=0.13) has relatively high rates of lactate and ammonia generation,
which is common for rapidly proliferating animal cells. To model a more effi-
cient stoichiometry, consider a (significant) improvement to Lac/Glc=0.94 and
bioreactor design principles and limitations 27
Figure 2.7: Fed-batch simulations in an air-sparged 20 m
3
bioreactor with 80% max working
volume and 5 mmol/L max NH
3
concentration. Dashed lines represent 6 doublings; solids
lines represent 2 doublings. (a) Lac/Glc=1.77 and Gln/Glc=0.13. (b) Lac/Glc=0.94 and
Gln/Glc=0.047.
Gln/Glc=0.047. Figure 2.8c shows a fed-batch simulation with this enhanced
metabolism, which begins at ~14.3 m
3
and a cell density of 0.2×10
6
/mL
(0.6 g/L). After 6 doublings, the final cell density is 12×10
6
/mL (36.3 g/L).
If the number of doublings is likewise limited to two, a final density of
16×10
6
/mL (47 g/L) can be reached. In this case, the batch endpoint is
reached simultaneously with the O2mass transfer limit.
These simulations can be extended to find the maximum cell density that
meets all above constraints at the end of a fed batch.
64
Figure 2.8a presents
64 Constraints summary:
Volume fraction φ<0.25
kLasuch that OTR=OUR at
us=0.006 m/s and λK20 µm
pCO2<100 mbar
Mixing time tm<1/kLa
NH3<5 mmol/L
Lac<50 mmol/L
this maximum supported cell density in air-sparged STRs from 1–200 m
3
. At
the baseline volume of 20 m
3
, the O
2
- and mixing-limited densities are roughly
equal at ~50 g/L.
65
In fact, the catabolic parameters above (Lac/Glc=0.94 and
65
For a 1,500 pg CHO cell, this mass den-
sity would be equivalent to ~30×10
6
/mL.
Gln/Glc=0.047) were selected to ensure that the NH
3
constraint would not
be incurred before this point. These are the maximum catabolic inefficiencies
that permit a 20 m
3
fed batch to stay under the likely inhibition levels of
lactate and ammonia such that the inhibitor-limited cell density is reached
simultaneously with another limitation (mixing, in this case). At smaller
volume, the O
2
and NH
3
limits dominate; at larger volume, the mixing time
dominates.
The pCO
2
limit is not incurred when sparging with air, though from
Figure 2.8a it is noted to have a strong dependence on bioreactor volume.
This is due to the constraint that was placed on the superficial velocity of
the sparge gas (0.006 m/s) in the constant-OTR approach. In sparged batch
or fed-batch culture, CO
2
is only removed by stripping into the bioreactor
exhaust. A constant-vvm scale-up approach can enhance stripping to mitigate
the pCO
2
limitation but may lead to excessive bubble-induced shear at very
large volume. In any event, the maximum supported cell density in an air-
sparged STR is only a fraction of the viscosity-limited density of 258 g/L.
bioreactor design principles and limitations 28
Figure 2.8: Maximum cell density achievable in fed-batch suspension culture at various bioreac-
tor sizes and with various limitations. The limiting density for each constraint was computed
independently of the others, and the density axis is truncated at the viscosity limit (Table 2.2).
(a) 21% O
2
sparge; Lac/Glc=0.94 and Gln/Glc=0.047. (b) 90% O
2
sparge; Lac/Glc=0.50 and
Gln/Glc=0.025.
ÉHigh-purity oxygen
Although an OTR approaching 200 mol O
2
/m
3
-h is common in an air-sparged
STR fermentor, the sparging and agitation limits of a cell culture bioreactor
effectively limit OTR to <~25 mol O
2
/m
3
-h when air is used. To obtain a
higher OTR (and thus a higher cell density), oxygen or O
2
-enriched air must
instead be sparged. In biopharmaceuticals manufacturing, the use of high-
purity oxygen is a simple economic decision. With such valuable products
and such small volumes, the benefits of increased cell density and product
titer far outweigh the cost of gas. At the scale of cultured meat, however,
the economics are less clear. Though a sufficiently large consumer (one that
requires O~1,000 kTA, such as a steel mill) can contract with an industrial
gas company to construct a dedicated air separation unit that provides pure
O
2
at ~$0.04/kg, the demand of a cultured-meat facility would not be nearly
this large. At smaller scale, high-purity merchant oxygen (delivered in trucks)
is far too expensive, given that as much as 80% of it will be vented from the
bioreactor. The scale of a cell-culture facility would be more consistent with
on-site production of 90% O
2
in a vacuum pressure-swing adsorption (VPSA)
unit, which has a size-dependent effective cost of $0.10–0.20/kg O
2
[130].
From Reaction 2.11, the stoichiometric demand of O
2
is 0.2 kg/kg wet cell
mass. Even if 80% of sparged O
2
were lost through the reactor vent, a single
facility producing 50 kTA of bulk cell mass could be served with a ~50 kTA
(4,000 Nm
3
/h) oxygen unit
66
and the cost contribution to cell mass would be
66Well within available capacity [131].
<$0.20/kg.
Reaction 2.11 was cited above because, to take advantage of higher O
2
purity, the catabolic efficiency must be further enhanced to Lac/Glc=0.50 and
Gln/Glc=0.025.
67
Figure 2.8b repeats the cell density calculation with 90%
67
These are the parameters used in Reac-
tion 2.10. Note that the ratio of Lac/Glc to
Gln/Glc must be 20 for the limits of 5 mM
NH
3
and 50 mM Lac to be reached simul-
taneously.
O
2
sparge gas and the enhanced metabolism, which was selected to cause the
NH
3
limit to occur at the same cell density as the pCO
2
limit at 20 m
3
. The
bioreactor design principles and limitations 29
maximum supported cell density at this volume is 40×10
6
/mL (120 g/L). At
larger volume, the pCO
2
limit is incurred, but the supported cell density with
90% O2remains significantly higher than with air.68
68
The mixing limitation has been pushed
to higher cell density because the criterion
for this limit is t
m
<1/k
L
a, and k
L
acan be
much lower when the O
2
concentration
driving force is high (Equation 2.15).
ÉPerfusion culture
Perfusion technology was developed as a higher-intensity alternative to batch
or fed-batch cultures in biopharmaceuticals manufacturing. In perfusion
culture (Figure 2.6b), the contents of the bioreactor are continuously cycled
through a cell retention device, e.g., a filter, gravity settler, or centrifuge.
Cells are returned to the bioreactor while the spent media perfuses out. Lost
nutrients are replaced by fresh media. Via the perfusate stream, extracellular
products are continuously harvested and inhibitors are continuously removed.
In many cases, the removal of inhibitors permits higher cell densities than are
achievable in fed-batch operation—in commercial perfusion cultures of CHO
cells, 100×106/mL is not unheard of, though 50×106/mL is more common.
Because they are limited by the capacity and efficacy of the cell retention
device, perfusion culture volumes are necessarily much smaller than the
volumes discussed above for fed-batch cultures. The alternating tangential-
flow (ATF) filter has near 100% cell retention and is commonly used for high
cell-density applications; its capacity is limited by the residence time of cells
inside the unaerated dead volume of the filter and its connecting piping [132].
The largest available can run at perfusion rates up to 1,000 L/d [133], though
practical perfusion rates may be lower, depending on cell density, culture
viscosity, and the desired cultured duration.
69
According to its manufacturer
69
Filters foul faster at a higher perfusion
rate.
(Repligen), the Xcell ATF 10 is capable for bioreactors up to 2 m
3
in a dual-
filter configuration, though several review papers indicate that commercial
perfusion culture sizes are rather closer to the 0.5–1 m
3
range [134,135]. If
the perfusion rate is expressed in units of reactor volumes per day,
70
Table 2.4
70Common units are RV/d, or d-1.
gives some practical limits for perfusion rate in various bioreactor sizes.
Table 2.4: Practical maximum perfusion
rates with ATF cell retention, at various
bioreactor sizes.
Volume ATF Perf. rate
0.5 m31×ATF 10 2.0/d
1 m31×ATF 10 1.0/d
1 m32×ATF 10 2.0/d
2 m32×ATF 10 1.0/d
At steady-state operation, cells are bled from the bioreactor (see Fig-
ure 2.6b) to maintain growth rate at
µmax
and avoid stress or senescence. At
a growth rate of 0.029/h, the cell bleed increases the effective perfusion rate
by 0.5–0.6/d, depending on cell density.
71
In principle, a semi-continuous cell
71
At relatively low cell density, devices
with higher throughput but lower cell re-
tention than an ATF (e.g., a centrifuge
or gravity settler) could be used for bulk
cell culture if the perfusate and cell bleed
streams were combined into a single out-
let. However, the cell density achievable
with these devices is much lower than the
>100 g/L density required for economic
cell production [133].
bleed could feed downstream processing operations such as tissue culture.
This downstream equipment could thus be rationally sized to the plant’s
average output, instead of being massively oversized to process a fed-batch
harvest before it dies. With continuous inhibitor removal, it would also seem
that perfusion might enable higher-density culture of metabolically inefficient
cell lines.
Figure 2.9 presents curves of achievable cell density in perfusion cultures
as a function of perfusion rate. The wild-type Reaction 2.9 generates 2 mmol
NH
3
/mol DCM
a
-h. If NH
3
were removed via the perfusate stream at a steady-
state NH
3
concentration of 5 mmol/L, then at a perfusion rate of 2.0/d it
can be computed that the inhibition limit is reached at a cell density of only
20 g/L (6.8×10
6
cell/mL). This density is significantly higher than predicted
bioreactor design principles and limitations 30