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\begin{document}

\title{Using MVDA with Stoichiometric Balances to Optimize Amino Acid
Concentrations in Chemically Defined CHO Cell Culture Medium for
Improved Culture Performance}



\author[1]{Taha Salim}%
\author[1]{Gaurav Chauhan}%
\author[2]{Neil Templeton}%
\author[1]{Wai Lam   Ling}%
\affil[1]{Merck \& Co Inc}%
\affil[2]{Merck and Co Inc West Point}%


\vspace{-1em}



  
  \date{June 18, 2024}


\begingroup
\let\center\flushleft
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\endgroup





\selectlanguage{english}
\begin{abstract}
Chemically defined (CD) media are routinely used in the production of
biologics in Chinese Hamster Ovary (CHO) cell culture and provide
enhanced raw material control. Nutrient optimized CD media is an
important path to increase cell growth and monoclonal antibody (mAb)
productivity in recombinant CHO cell lines. However, nutrient
optimization efforts for CD media typically rely on multi-factorial and
experimental design of experiment (DoE) approaches or complex
mathematical models of cellular metabolism or gene expression systems.
Moreover, the majority of these efforts are aimed at amino acids since
they constitute essential nutrients in CD media as they directly
contribute to biomass and protein production. In this study, we
demonstrate the utilization of multi-variate data analytics (MVDA)
coupled with amino acid stoichiometric balances (SBs) to increased cell
growth and mAb productivity in efforts to reduce CD media development
efforts. SBs measure the difference between theoretical demand of amino
acids and the empirically measured fluxes to identify metabolic states
of the cell. When coupled with MVDA, the statistical models were not
only able to highlight key amino acids towards cell growth or
productivity, but also provided direction on metabolic favorability of
the amino acid. Experimental validation of our approach resulted in a
55\% increase in total cell growth and about an 80\% increase in total
mAb productivity. Increased specific consumption of stoichiometrically
balanced amino acids and decreased specific consumption of glucose was
also observed in optimized CD media suggesting favorable consumption of
desired nutrients and a potential for energy redistribution towards
increased cellular growth or mAb productivity.%
\end{abstract}%



\sloppy


\textbf{Using MVDA with Stoichiometric Balances to Optimize Amino Acid
Concentrations in Chemically Defined CHO Cell Culture Medium for
Improved Culture Performance}

Taha Salim

Senior Scientist

Merck \& Co. Inc.

Kenilworth, NJ, USA

(201) 982-0330

Email: Tsalim786@gmail.com

Gaurav Chauhan

Principal Scientist

Merck \& Co. Inc.

Kenilworth, NJ, USA

(240) 308-4173

Email: Gaurav.chauhan1@merck.com

Neil Templeton

Associate Principal Scientist

Merck \& Co. Inc.

West Point, PA, USA

(434) 665-8060

Email: neil.templeton@merck.com

Wai Lam W. Ling\textsuperscript{1}

Senior Principal Scientist

Merck \& Co. Inc.

Kenilworth, NJ, USA

(646) 627-5525

Email: wai\_lam.ling@merck.com

1. Wai Lam Ling has recently changed affiliations to Head of MS\&T at
Rocket Pharma (Cranbury, NJ, USA). Her updated email address is
wling@rocketpharma.com

\textbf{Using MVDA with Stoichiometric Balances to Optimize Amino Acid
Concentrations in Chemically Defined CHO Cell Culture Medium for
Improved Culture Performance}

*Taha Salim \textsuperscript{a}; *Gaurav Chauhan \textsuperscript{a};
Neil Templeton \textsuperscript{b}; Wai Lam W. Ling \textsuperscript{a}

\textsuperscript{a} Merck \& Co., Inc., Kenilworth, NJ, USA

\textsuperscript{b} Merck \& Co., Inc., West Point, PA, USA

* Equal Contribution

\textbf{Abstract}

Chemically defined (CD) media are routinely used in the production of
biologics in Chinese Hamster Ovary (CHO) cell culture and provide
enhanced raw material control. Nutrient optimized CD media is an
important path to increase cell growth and monoclonal antibody (mAb)
productivity in recombinant CHO cell lines. However, nutrient
optimization efforts for CD media typically rely on multi-factorial and
experimental design of experiment (DoE) approaches or complex
mathematical models of cellular metabolism or gene expression systems.
Moreover, the majority of these efforts are aimed at amino acids since
they constitute essential nutrients in CD media as they directly
contribute to biomass and protein production. In this study, we
demonstrate the utilization of multi-variate data analytics (MVDA)
coupled with amino acid stoichiometric balances (SBs) to increased cell
growth and mAb productivity in efforts to reduce CD media development
efforts. SBs measure the difference between theoretical demand of amino
acids and the empirically measured fluxes to identify metabolic states
of the cell. When coupled with MVDA, the statistical models were not
only able to highlight key amino acids towards cell growth or
productivity, but also provided direction on metabolic favorability of
the amino acid. Experimental validation of our approach resulted in a
55\% increase in total cell growth and about an 80\% increase in total
mAb productivity. Increased specific consumption of stoichiometrically
balanced amino acids and decreased specific consumption of glucose was
also observed in optimized CD media suggesting favorable consumption of
desired nutrients and a potential for energy redistribution towards
increased cellular growth or mAb productivity.

\textbf{Keywords}

Stoichiometric Balances

Multivariate Data-Analytics

Orthogonal Partial Least Squares

Amino Acid Consumption Rates

Cell Culture Media Development

\textbf{Introduction}

Improved robustness in production of monoclonal antibodies (mAbs) from
Chinese Hamster Ovary (CHO) cell culture processes depends on gaining
better understanding of biological changes, interactions, and impact to
product quality and yield. Advances in systems biology have led to the
development of computational tools to compliment emerging technologies
that can perform data-rich experimentation (Schaub, Clemens, Kaufmann,
\& Shulz, 2011; Sharma, Tripathi, \& Mukherjee, 2016). As a result, the
employment of computational tools such as empirical or mathematical
modeling have gained acceptance as a potential path to provide a deeper
understanding of cellular mechanisms to inform process decisions that
result in more efficient experimental practices during pre-commercial
biologics development (Insaidoo, Banerjee, Roush, \& Cramer, 2017; Roush
et al., 2020; Smiatek, Jung, \& Bluhmki, 2020). For instance,
computational efforts have shown great potential in optimizing nutrient
concentrations within chemically defined (CD) media for CHO cells by
modeling routine cell culture and metabolomic data to highlight key
limiting nutrients (Cuperlovic-Culf \& Culf, 2016). Optimizing base and
feed media compositions is a critical step of process development as
components in these media directly impact critical quality attributes
and cellular productivity of mAbs (Li, Vijayasankaran, Shen, Kiss, \&
Amanullah, 2010). However, despite long-term benefits of raw material
control and cost reduction, development of proprietary CD media is a
resource-and time-intensive process which requires a significant number
of experiments (Kelley, 2009). By leveraging historical data in
computational algorithms, process development researchers are able to
identify key components in media that can significantly reduce the
complexity of large experimental designs and reduce the development time
to optimize media (Torkashvand et al., 2015; Xing et al., 2011).

In this study, we explored the utilization of multivariate data
analytics (MVDA) modeling to optimize amino acid concentrations in CD
feed media with aims to increase cell growth and mAb productivity. While
other components in CD media such as vitamins, trace elements, and
co-factors are required for various cellular functions, amino acids are
considered one of the most important component group in CD media
representing about 74\% of CHO cell mass (Carrillo-Cocom et al., 2015;
Fan et al., 2015; Pan, Streefland, Dalm, Wijffels, \& Martens, 2017;
Templeton, Xu, Roush, \& Chen, 2017a). Balancing and optimizing amino
acid concentrations therefore is critical to ensure CD media can sustain
cell growth and mAb productivity. Thus far, majority of laboratory-based
experimental and computational approaches for optimizing amino acid
levels in CD media have been built on supplementing the amino acids that
were being consumed in excess (Dietmair et al., 2012; Duarte et al.,
2014; Robitaille, Chen, \& Jolicoeur, 2015a). A challenge with such an
approach is that over supplementation and consumption of certain amino
acids can lead to the production of harmful byproducts. For instance,
varying the amount of essential amino acid concentrations can lead to
the differential regulation of amino acid metabolic pathways that could
ultimately result in increased formation of harmful byproducts such as
lactate or ammonia (Alden et al., 2020; Morris et al., 2020; Park,
Reimonn, Agarabi, Brorson, \& Yoon, 2018; Pereira, Kildegaard, \&
Andersen, 2018). Alternatively, supplementing amino acids in a
time-dependent manner based on cell demand would ensure optimal
consumption and cellular metabolism presumably resulting in better cell
growth and mAb productivity.

In aims to understand the dynamics of amino acid metabolism, Xie and
Wang described the relationship between the theoretical demand and the
actual consumption of amino acids as their stoichiometric balances (Xie
\& Wang, 1994b; Xie \& Wang, 1994c). According to their work, the
theoretical demand of an amino acid is the amount needed to maintain
both biomass and mAb productivity per cell, and with a steady state
approximation, the amount consumed is balanced stoichiometrically with
the theoretical demand. However, recent work on CHO cell amino acid
requirements showed that most cells do not behave in a steady state and
that the production process by which nutrient feeds are provided can
greatly modulate the dynamics of consumption (Kyriakopoulos, Polizzi, \&
Kontoravdi, 2013; Luo et al., 2020). Templeton et al described the
existence of two possible metabolic states. Within the first state, the
actual consumption of an amino acid exceeds the theoretical demand
resulting in a catabolic state in which the cell can breakdown the
excess nutrients for energy or biomass. In contrast, within the second
state, the theoretical demand exceeds the actual consumption of an amino
acid resulting in an anabolic state in which the cells must
biosynthesize or acquire the required nutrients (Table 1) (Templeton,
Xu, Roush, \& Chen, 2017b). Time-dependent dynamics of amino acid
stoichiometric balances can therefore highlight concentration
constraints and metabolic requirements for different amino acids
throughout the culture (Ahn \& Antoniewicz, 2011; Pan, Dalm, Wijffels,
\& Martens, 2017a). Although a stoichiometric-based model can provide a
systematic and mathematical approach to balancing component composition
in CD media, it does not eliminate the resources, and time needed for
experimental work (Kumar, Bhalla, \& Rathore, 2014). Accordingly,
computational MVDA approaches have shown potential in utilizing
historical cell culture data and nutrient consumption rates to minimize
the resource demand of lab-based experimental designs and execution
(Suarez-Zuluaga, Borchert, Driessen, Bakker, \& Thomassen, 2019).

MVDA methods rely on a dimensional reduction strategy in which
information from a group of variables can be consolidated and summarized
into latent variables that in turn, can help describe the overall
distribution of experimental observations (i.e. culture time points,
cell culture batches) (Mevik \& Wehrens, 2007). Each latent variable is
based on the individual contribution of variance from all of the
variables within the group, and variable ranking statistics can
therefore be used to highlight and sub-select a set of key variables
towards specific response parameters (Prieto, Eriksson, \& Tyrgg, 2014).
As a result, MVDA approaches can be used to analyze batch-to-batch
variability, test the impact of culture performance from process
variations, and identify key nutrients from cell culture media (Nitish
\& Rathore, 2011). In addition, statistical MVDA models in bioprocess
rely on the ``black box'' approach in correlating extracellular
metabolites and fluxes to cellular phenotypical behavior without
mathematically modeling the intracellular complexities of cellular
metabolism (Kanehisa \& Goto, 2000; Noll \& Henkel, 2020). Accordingly,
MVDA models are easier to develop, do not require systematic constraints
or curation of biological parameters, and are computationally efficient
in determining key correlations (Rouiller et al., 2013).

Several MVDA algorithms that are routinely used within bioprocess
development include Principal Component Analysis (PCA), Partial Least
Squares (PLS) Regression, and variations of PLS such as Orthogonal
Partial Least Squares (OPLS) (Mevik \& Wehrens, 2007; Yamamoto et al.,
2009). For instance, Kirdar et al utilized PCA to diagnose similarities
and differences between small-scale and large-scale manufacturing
batches for biopharmaceutical products (Kirdar, Conner, Baclaski, \&
Rathore, 2007). Dietmair et al utilized PLS to determine a range of
metabolites in the culture medium that correlate with the cell growth
rate (Dietmair et al., 2012). In most cases, MVDA models have provided
support in upstream bioprocess development, process characterization,
platform development, and more recently, media development that drive
specific responses (Behrouz et al., 2020; MKS Umetrics AB, 2013; Pybus
et al., 2014; Worley \& Powers, 2013). Therefore, we hypothesized that
amino acid stoichiometric balances (SB) used in combination with MVDA
models, could not only highlight key amino acids, but also provide
information on cell culture performance characteristics. While SB may
not be able to identify specific intracellular pathways or enzyme
activation due to amino acid changes, it may however serve as an
effective surrogate to extrapolate the intracellular ``black box''
activities that result in the detected culture outcomes. Furthermore, we
postulate that supplementing stoichiometrically desired amino acids that
are positively correlated to cell growth or mAb productivity would help
improve the desired cell culture performance. The amino acid enrichment
`cocktails' can then be designed and established based on SB and MVDA
for a defined or training set of culture runs and may be used as feed
supplements for future or subsequent culture runs.

In support of our hypothesis, we trained an MVDA model using a 25-batch
study in which cells were supplemented with various amounts of a high
nutrient feed in aims to identify metabolite stoichiometric balances
predictive of cell growth or mAb productivity. Model-derived key
stoichiometric balances were translated into amino acid cocktail feeds
and supplemented at model-informed time points. In addition to the feed
media used in the training set, the model-generated amino acid cocktail
feeds were also tested as supplements for two other chemically-defined
feeds at lower nutrient concentrations, referred to as moderate and low
nutrient feeds. Moderate and low nutrient feeds contained 40\% and 17\%
of the carbon concentration relative to the high nutrient feed level.
Experimental validation of our platform and model-directed amino acid
supplementation showed about a 20\% increase in cumulative viable cells
(CVC) and a 30\% increase in mAb titer within the supplemented high
nutrient condition, about a 30\% increase in CVC and 80\% increase in
titer within the supplemented moderate nutrient condition, and about a
55\% increase in CVC and 80\% increase in titer within the supplemented
low nutrient condition. Results from our study provide evidence towards
a novel method to help improve and streamline CD media development for
bioprocess.

\textbf{Materials and Methods}

\emph{Cell Line and Expansion}

A GS CHO cell line expressing a proprietary monoclonal antibody (mAb)
was used for this study. The seed train was initiated from a vial thaw
and scaled up in shake flasks to generate enough cells for production
bioreactors. Cell expansion was carried out in CD CHO medium (Gibco, NY)
and routinely passaged to maintain exponential growth. The shake flasks
were maintained in shaking incubators at 36.5\selectlanguage{ngerman}°C, 5\%
CO\textsubscript{2}, 70\% humidity, and 100 RPM.

\emph{Cell Culture and Media}

A total of 25 14-day fed-batch production cell culture conditions were
used to build a training dataset for the model. For all 25 batches, CHO
cells were cultured in AMBR® 15 (Sartorius Stedim, GE) mammalian
bioreactors seeded at 2E6 cells/mL with an initial working volume of 13
mL. Bioreactors were operated at dissolved oxygen of 30\%, pH setpoint
of 6.95±0.15 controlled by either CO\textsubscript{2} or base addition,
agitation at 900 RPM, and incubated at 36.5°C. Control cultures were fed
with a high nutrient feed based on a previously defined process. The
remaining cultures were fed varying amounts of the same high nutrient
feed following the same feeding schedule to obtain a varying
distribution of growth and productivity profiles for the training
dataset. Glucose was supplemented back to 6 g/L if extracellular glucose
levels fell below 3 g/L. Similarly, glutamic acid was supplemented as 3
mM bolus additions if the extracellular glutamic acid levels fell below
4 mM.

To validate the MVDA models for cell growth and mAb productivity, an
experiment containing 46-batches was performed. Three baseline controls
were designed in which cells were fed with three CD feed media
corresponding to high, moderate, and low nutrient levels. In addition to
the ranging nutrient feeds (high, moderate, and low), key amino acids
identified from either the growth or production model were formulated
into amino acid cocktail feeds and supplemented to the cultures at
model-informed time points.

Each cocktail feed contained a 100X concentration of the specific amino
acids with pH adjusted via 10N NaOH to maintain solubility. Previous
studies indicated that AMBR® 15 bioreactors incur a 1 -- 1.5\% of
evaporation rate (v/v per day), which can lead to inaccurate
quantification of cell growth and mAb productivity due to the small
working volume (Hsu, Aulakh, Traul, \& Yuk, 2012). Therefore, 150 \selectlanguage{greek}µ\selectlanguage{english}L of
sterile water was supplemented daily to compensate for evaporation. To
compensate for osmotic and pH differences of amino acid cocktails,
control solutions with similar osmolality and pH to the most
concentrated amino acid cocktail feed were added at the same volume. In
addition, a control was included to confirm the impact of basal media
dilution.

Cell culture samples were taken on alternate days up to and including
day 14 for offline analysis of VCD, cell viability, cell diameter, pH,
pCO\textsubscript{2}, extracellular metabolites (lactate, ammonia,
glutamate, glutamine, and glucose), mAb titer, and amino acids. Viable
cell density, viability, and cell diameter were measured using the
trypan blue exclusion method on a CEDEX HiRes cell counter (Roche
Diagnostics GmbH, Mannheim, Germany). The ABL80 blood gas analyzer
(Radiometer, Denmark) was used to capture offline pH and pCO2 values.
The extracellular metabolites were measured using the RX IMOLA Clinical
Chemistry Tester (Randox, UK). Antibody titer was quantified using a
previously described protein-A reverse-phase high-performance liquid
chromatography (HPLC) method (Hoshan et al., 2019). Amino acids were
measured using Waters Acquity ultra-performance liquid chromatography
(UPLC) H-Class Bio System with an AccQ-Tag Ultra Derivatization Kit
(Waters, MA). The amino acid standard kit (A9781) was obtained from
Millipore Sigma (St. Louis, MO).

\emph{Statistical Analysis and Empirical Modeling Methods}

Experimental conditions were performed in biological replicates and
resulting data is presented with the standard error of the mean. CVC and
mAb titer were normalized to the maximum CVC and titer of the respective
process control conditions. Graphical analysis, standard error
calculations, ANOVA, and one-way student's t-tests were performed in
Microsoft Excel and SAS JMP (SAS, USA), respectively.

SIMCA-P+ (Sartorius Stedium, GE) was used for MVDA modeling and detailed
methods for PCA and PLS regression are described by Wold et al (MKS
Umetrics AB, 2013). However, in short, multi-variate methods begin with
dimensional reduction where high-dimensional datasets can be reduced to
a lower dimensional space and be explained by fewer variables (i.e.
latent variables). The latent variables are calculated by unit
normalization of the data followed by a projection of the normalized
data on a lower dimensional space, and lastly finding the directions of
the greatest variance within that space or the eigen vector (Mevik \&
Wehrens, 2007). The total variable contribution towards the greatest
variance in any given direction is described by the first latent
variable or in the case of PCA, the first principal component. Every
subsequent component within a PCA model is orthogonal or perpendicular
to the preceding component and is aimed at explaining the total variance
of a dataset. Accordingly, each component is a summation of the
individual variable contributions or loadings towards the variance.
Interestingly, Wold et al found that the sum of every variable
contribution across all the components in a model could be represented
as a variable importance to projection (VIP) which can provide a
heuristic multivariate ranking system (Akarachantachote, Chadcham, \&
Saithanu, 2013; Prieto et al., 2014). As a result, dimensional reduction
models can be used to not only provide a holistic distribution of
batches or even individual observations, but also identify key variable
contributions that explain the distribution between observations and
ultimately, pose as potential targets for optimization efforts.

In contrast, the calculation of latent variables is modified when using
supervised approaches such as PLS, as the goal for latency is the
direction of the greatest co-variance between the explanatory variables
and the response variable(s). Since the first predictive component in a
PLS model is not the first principal component, PLS models become very
powerful when there is a high degree of collinearity between the
explanatory variables and the response variable. However, when the
variables are nonlinear in behavior, such as in the case of amino acid
stoichiometric balances, the goodness of fit (R\textsuperscript{2}) and
the goodness of prediction (Q\textsuperscript{2}) of a PLS model are
significantly impacted as a high degree of information is unaccounted
for in the explanatory variable space. To circumvent this issue,
Orthogonal Partial Least Squares (OPLS) was used in which the first
component or the predictive component is forced to be the first
principal component and every subsequent orthogonal component aims to
explain the remaining co-variance between the explanatory and response
variables. Consequently, OPLS models yield better predictions and
increased model interpretability towards nonlinear response variables as
a greater degree of information in the explanatory variable space is
considered (Bylesjo M et al., 2006; Yamamoto et al., 2009). Accordingly,
OPLS models built with stoichiometric balances were found to have higher
Q\textsuperscript{2} values than PLS models (data not presented).

Lastly, to incorporate the time-dependent contributions of the amino
acid consumption rates and resulting stoichiometric balances, the
training set data matrix was transformed to a batch-level model (BLM)
format. In a BLM format, every variable at every day measured across the
batches was formatted to become an independent variable. As a result,
each row of a BLM data matrix represented a single batch with every cell
culture variable expanded by the number of timepoints it was measured as
additional columns, forming a wider and shorter data matrix. The
benefits of the BLM format over the untransformed dataset format were
two-fold: (1) each variable in the model was able to provide a specific
time-dependent contribution that was representative of a particular
instance in a batch and (2) increased precision with the OPLS algorithm
as each component of the model is a weighted average of all the
variables and increased number of variables provided a greater
reliability towards the calculation of that weighted average (Vajargah,
Sadeghi-Bazargani, Mehdizadeh-Esfanjani, Savadi-Oskouei, \& Farhoudi,
2012; Worley \& Powers, 2013; Worley \& Powers, 2015). For instance, all
20 amino acid stoichiometric balances that was captured from the 25
training batches were measured every other day from day 0 to day 14 and
interpolated for the unmeasured days resulting in 15 observations per
batch or 375 observations across all 25 batches. But when transformed
into a BLM format, the 20 original stoichiometric balance variables were
expanded to 300 variables capturing the stoichiometric balance at each
time point (day 0 -- day 14) and the observations collapsed to 25 rows
representing one observation per batch. The complexity and
interpretation of the resulting matrix was drastically reduced into
latent variables using the dimensional reduction thus highlighting the
benefit of MVDA modeling capabilities and its ability to retain
biological time-dependent information for a large set of variables to
rapidly identify key modulators to improve bioprocess development
efforts.

\textbf{Results}

OPLS models were built to predict cell growth or mAb expression as a
function of amino acid stoichiometric balances. Since cell growth was
measured as viable cell density (VCD) throughout the culture, CVC was
calculated to quantify the total cells that were present within a given
time interval. VCD profiles of CHO cell culture typically follow four
growth phases, namely, lag phase, log phase, stationary phase, and death
phase (Dutton, Scharer, \& Moo-Young, 2006). Similarly, in the training
dataset, VCD profiles of the 25 batches also reflected the same four
phases but varied drastically in peak cell densities (black lines in
Fig. 1a). Peak VCD was observed at day 9 for majority of the training
batches with the exception of a few that peaked near day 7 representing
those batches that received a lower percentage of the high nutrient
feed. In contrast, CVC profiles increase over time as they represented a
growing sum of total in the culture (green lines in Fig. 1a).
Intuitively, modeling the time at which peak VCD was reach or the end of
the log phase would highlight the time-dependent contributions by amino
acids from the start of the culture which would produce a model with
narrower utility. Since \textgreater{}75\% of the training runs showed
day 9 as peak VCD and the remaining runs also achieve highest total
cells on day 9, the CVC at day 9 was chosen as the response variable for
the growth model. A similar OPLS model was created to predict titer but
in contrast to VCD, mAb titer was measured as the cumulative total
concentration of mAb within the culture at any given time. Since peak
mAb titer was observed by the end of all cultures, day 14 titer was
chosen as the response variable for the production model (Fig. 1b).

To measure the variability and generalization of a model prediction, a
relatively large distribution space was required in the training
dataset. Accordingly, the amino acid SBs from the 25 training batches in
a BLM format were analyzed by PCA. Each observation or score of the PCA
model in BLM format, which represented a single batch, was graphically
analyzed in a score plot and the 375 amino acid SBs were analyzed in a
loadings plot to identify any collinearity or dependencies of the
variables within the datasets that could possibly bias the prediction
(Fig. 1c and Fig. 1d). The PCA model explained 38.8\% variance in the in
the first component and 14.7\% variance in the
2\textsuperscript{nd}component (Fig. 1c). Although only two components
are graphed, a 5-component model was built to ensure greater than 70\%
of variance was captured to represent the majority of the dataset.
However, based on the first two components alone, the distribution of
the batches showed a random dispersion and lack of any specific
clustering. In addition, the variable loadings plot did not highlight
any time-dependent grouping, suggesting a minimal collinearity or
internal bias within the training dataset in terms of amino acid SBs
(Fig. 1d). The generalized distribution of the variables provided a
strong potential for the OPLS model to learn and predict across a
varying space for future batches. The reliability of the PCA model was
further justified by the criteria to remove any outliers that could
cause internal biases. Accordingly, a 95\% Hotelling's
T\textsuperscript{2} ellipse was provided as a confidence interval
around the dataset to identify any batches that deviated from the
majority (Rencher, 1993).

To ensure a strong fit for both models without a significant loss of
predictive power, the OPLS model for day 9 CVC was built with 1
predictive component and 9 orthogonal components resulting in a
R\textsuperscript{2} of 0.912 and Q\textsuperscript{2} of 0.726
(Supplementary Fig. S1a). The requirement of additional orthogonal
components was further reflected by the diverse spread of CVC profiles
throughout the 25 training batches ranging between 25E6 -- 45E6
cell-days per mL at day 9. Similarly, there was a large distribution of
day 14 titer ranging from 0.2 to 1.05 relative titer values (Fig. 2b).
Accordingly, the OPLS model for day 14 Titer had 1 predictive component
and 6 orthogonal components with R\textsuperscript{2} of 0.832 but a
Q\textsuperscript{2} of 0.422. Although the predictive power of the
production model to generalize to diverse future batches was not as
strong as that of the growth model, it was able to highlight information
on key variables for media optimization (Supplementary Fig. S1b).

\emph{Identifying Variable Importance with Stoichiometric Balances}

Since amino acid SBs provided information on the cellular metabolic
state in terms of amino acid consumption, model-predicted key amino acid
additions at specific time points provided the potential to improve cell
growth and mAb productivity. However, to identify key stoichiometric
balances from the growth model and the mAb production model, three
aspects had to be considered: (1) a variable ranking heuristic that
could provide a mathematical method to evaluate the importance of each
variable at a given time point; (2) a directionality coefficient that
could provide information on each variable's relationship towards the
response variable; and (3) the direction of the stoichiometric balance
since positive and negative balances represented two distinct metabolic
states. First, since each component in an OPLS model is described by a
weighted contribution of each variable in the dataset, the cumulative
squared sum of all the weighted contributions of each variable across
all the components was calculated to represent the variable importance
to projection (VIP). Since the VIP is a squared sum always resulting in
a positive magnitude, the VIP was used as a ranking system for all the
variables in terms of importance to the predictability of the model.
Moreover, Powers et al described that the average VIP value compared
across all variables is typically around 1 (Powers et al., 2020).
Accordingly, VIP values greater than 1 were selected to be variables
that significantly contributed towards the predictability of the
response variable whereas those with a VIP less than 0.5 were presumed
to have nominal contributions to the overall model. Variables with VIP
values between 1 and 0.5 added to the accuracy and reliability of the
model however did not significantly contribute to the predictive power
of the model. Second, correlative directionality for each variable was
averaged across all the components and represented as the magnitude and
directionality of each variable's coefficient. In such a case,
positively correlated values represented those stoichiometric balances
that would increase co-dependently with the response variable regardless
of the actual magnitude of the variable. Lastly, since stoichiometric
balances could exist either as a positive value representing greater
consumption than the theoretical demand or a negative value representing
a lack of consumption compared to the theoretical demand, the
directionality of the stoichiometric balance was used to distinguish
between nutrient rich and nutrient limited conditions. However, since
the model-selected amino acid SBs were the weighted sums across all the
batches, the directionality sign of the amino acid SBs was based on the
process control from the training dataset. Accordingly, Table 2 shows
the directionality signs of all the amino acid SBs from the process
control condition and provides the reference values for biomass and mAb
composition for each amino acid.

Based on the selection factors for variable importance, three distinct
experimental criteria emerged for SBs to validate the growth and
production models. The first Criterion consisted of positively
correlated SBs with a VIP greater than 1 and a positive stoichiometric
balance sign representing amino acids that are being favorably consumed
greater than the theoretical demand. The second Criterion consisted of
positively correlated stoichiometric balances with a VIP greater than 1
and a negative stoichiometric balance sign representing amino acids that
are being favorably consumed less than the theoretical demand. The third
Criterion consisted of positively correlated stoichiometric balances
with a VIP less than 0.5 and a negative stoichiometric balance sign also
representing amino acids that are being favorably consumed less than the
theoretical demand but deemed unimportant by the model. For each
Criterion however, the sign of the magnitude of the stoichiometric
balance was representative of the process control cultures of the
training dataset as opposed to the average across all the training
batches as the goal of the model was to improve cell growth and mAb
production beyond the current benchmark (Table 1). In all cases however,
negatively correlated stoichiometric balances were disregarded since
removing nutrient components from an existing chemically defined medium
poses a greater operational challenge than supplementing additional
nutrients. Therefore, the scope of this study focused only on positively
correlated stoichiometric balances.

For both the growth model and production model, scaled positive
coefficients from OPLS were plotted for each time-dependent
stoichiometric balance grouped by amino acid (Fig. 2). For each plot,
the variables displayed included those that fell within the VIP factor
for each Criterion and the variables highlighted included those that met
the stoichiometric balance sign factor for each Criterion (Growth Model:
Orange Bars; Production Model: Green Bars). For each model and
Criterion, amino acid cocktail feeds were developed for the
corresponding day based on the highlighted amino acid SBs.
Interestingly, most variables for both the growth and the production
models for Criterion 1 had positive stoichiometric balance signs (Fig.
2a and Fig. 2b). This was representative of the high nutrient feed
conditions since amino acids can routinely be saturated within the
extracellular environment. However, Criterion 1 was designed to measure
the effectiveness of providing an increased concentration of amino acids
already being consumed beyond the theoretical demand. For Criterion 2,
only a few variables were highlighted as important based on negative
stoichiometric balance signs. For instance, only alanine (days 1, 2, 4,
5, 6, and 7), cystine (days 3, 4, 6, 7, and 8) , and glycine (days 1, 2,
3, and 7) were identified as important for the growth model (Fig. 2c)
whereas the same variables with the addition of lysine (day 9) and
methionine (day 9) were identified as important in addition to the
former three for the production model (Fig. 2d). Interestingly, the high
crossover of amino acids identified between the production model and the
cell growth model supports the notion that increased total cells would
produce increased antibody. Criterion 3, on the other hand, was
primarily designed to measure the heuristic property of the VIP value
and thus, served as a negative control. Only those stoichiometric
balances were selected that provided minimal contribution to the
predictive power of the model. The selected Criterion 3 amino acids were
like that of Criterion two but were found important on different days
providing additional justification that stoichiometric balances can also
help highlight when a specific nutrient demand is needed by the cells
(Fig. 3e and Fig. 3f).

\emph{Experimental Validation with Amino Acid Supplementation}

To validate the OPLS Model for each Criterion, experimental conditions
were designed similarly to the high nutrient process control with the
addition of amino acid cocktail feeds. CHO cell cultures fed with amino
acid cocktails based on Criterion 1 showed a nominal increase in total
cell growth at day 9 for both models (Growth Model vs Control: no
significant change; Production Model vs Control: no significant change)
(Fig. 3a). Day 14 CVC was also analyzed to assess if the early additions
of amino acid up to day 9 would have an impact on the overall cell
growth of the culture. Similar to day 9, there was only a slight
increase of less than 10\% in totals cells from the growth model (p =
0.1712) suggesting that increased supplementation of amino acids that
were already being consuming in excess based on the theoretical demands
did not further drive cell growth. In some instances, overfeeding
nutrients can have deleterious effects on the cell culture (Salazar,
Keusgen, \& von Hagen, 2016). For instance, the growth model showed a
significant drop in titer near 20\% (p \textless{} 0.05) and a slight
drop in titer for the production model (p = 0.159) (Fig. 3b). For
comparison, day 9 titer was also analyzed to determine if the growth
model for Criterion 1 had any early impact on productivity.
Unfortunately, no deviation from the control was observed (Growth Model
vs Control: no significant change; Production Model vs Control: no
significant change).

In contrast, Criterion 2 was designed to test those amino acids that
were being consumed below their theoretical demand. However, since
Criterion 2 was built on a basis of high nutrient feeds in the training
dataset, we postulated that information gained could also support
various phases of media development such as moderate nutrient or low
nutrient feeds. Therefore, three feed media conditions for the growth
and production models were included with biological replicates for the
validation run. Similarly to Criterion 1, amino acid cocktail feeds were
prepared and supplemented on model-informed days. For statistical
comparisons of the model conditions to the control, CVC and relative
titer values were only considered from day 8 to day 14 because a
majority of the cultures showed similar CVC and mAb titer during the
first half of the culture. Although day 9 CVC did not show a significant
change for high nutrient conditions, day 14 CVC showed a modest increase
of about 10\% for the growth model and about 20\% for production model
(Fig. 4). A more significant increase was observed within the moderate
nutrient and low nutrient conditions when supplemented with the same
amino acid cocktail feeds. Increase in CVC was noticed as early as day 7
for both models in the moderate nutrient condition reaching about a 35\%
increase in total cells by day 14 for the growth model (p \textless{}
0.001) and about 30\% increase for the production model (p \textless{}
0.05). The low nutrient condition also showed an increase in CVC as
early as day 7 but relative cell growth propagated to near 55\% increase
in total cells for both models by day 14 (Growth Model vs Control: p
\textless{} 0.01; Production Model vs Control: p \textless{} 0.05).
Interestingly, the relative cell growth rates were only slightly
impacted by the amino acid supplementations (Fig. S3). The growth rate
for high nutrient conditions showed a minor increase at day 3 during the
log-phase of growth but also maintained the slight increased up to day 7
(p \textless{} 0.05) which could have been the driver to the 20\%
increase in CVC. Similarly, the growth rates for moderate and low
nutrient conditions also slightly increased, but unlike the high
nutrient condition, the growth rate remained elevated for a longer
duration up to day 9. Moderate nutrient conditions had a 5\% increase in
growth rate at day 3 in the growth model whereas the low nutrient
condition had a 5\% increase around day 5 reflecting a delayed log-phase
but overall greater increase in CVC relative to the control.

The increase in cell growth for both models was further reflected in mAb
productivity. Although the high nutrient growth model did not result in
any significant increase in titer, the production model yielded about
25\% increased productivity (p = 0.163) (Fig. 4). The moderate and low
nutrient productivity in contrast reflected a significant increase in
cell growth by producing about 80\% more relative titer by day 9 and
60\% more relative titer by day 14 when compared to control cultures (p
\textless{} 0.001). Although low nutrient conditions had a higher boost
in cell growth, it also resulted in a similar 60\% increase in
productivity by day 14 suggesting an upper threshold for mAb production
by this cell line with those particular feeds. The large increases in
mAb titer for moderate and low nutrient conditions were further
reflected by the significant increases in relative specific productivity
(qP) (Fig. S2). For example, the moderate nutrient condition showed a
20\% increase in qP for the growth model (p \textless{} 0.05) and showed
a near 30\% increase for the production model during the stationary
phase (p \textless{} 0.01). In contrast, the low nutrient condition
showed about a 40\% increase in qP starting from day 7 (p \textless{}
0.05) suggesting the increased mAb production was not just an artefact
of increased cell growth.

To further understand the differences between the resulting cell growth
and mAb productivity phenotypes observed, glucose consumption rates were
analyzed to assess how the model-driven conditions and supplementation
of presumably limiting amino acids could alter cellular metabolism.
Posed differently, was differential glucose consumption artefact of the
increased percentage of cells within each model condition or a result of
altered metabolic activity at the cellular specific level? Total glucose
consumption within high nutrient feeds did not show any change in
overall consumption whereas under moderate and low nutrient conditions,
there was about a 2 g/L decrease in peak glucose consumption (Fig. 5).
In contrast, the specific glucose consumption rates highlighted a more
significant difference between control and model conditions within
moderate and low nutrient feeds. Growth and production model conditions
resulted in almost a 1000 pmol/cell*day decrease in specific glucose
consumption in moderate feed and about a 2000 pmol/cell*day decrease in
low nutrient feeds (p \textless{} 0.01). Accordingly, the marked
increase in cell growth and mAb production for moderate and low nutrient
conditions when compared to the high nutrient condition was further
reflected by the larger magnitude of specific glucose consumption. Taken
together, the decreased specific glucose consumption rates in
model-driven conditions suggests that cells within these conditions
presumably consumed other nutrients such desired amino acids for
bioproduction and energy generation that ultimately resulted the cells
to be in a higher metabolic state to produce more mAb.

Since the amino acid cocktails were supplemented in addition to process
feed media and prepared at 100x concentrations, modulations in feed
volume, pH, and osmolality were warranted. Specific control conditions
for each model at all three nutrient feed levels for Criterion 2 were
included within the experiment to understand if the increase in CVC or
productivity was in fact due to the amino acids and no other cell
culture variations. The solution/pH control was designed for the high
nutrient feed only and was supplemented with base at the same volume and
pH as the amino acid cocktail with time points representative of either
of the growth or production models. Similarly, osmolality control
cultures were fed with a NaCl solution with the same osmolality and
volume as the highest osmolality among the amino acid feed cocktails.
High nutrient feed cultures supplemented with the solution/pH control
feed showed about a 20\% decrease in day 14 CVC and day 14 titer (Fig.
S3). Due to the high pH levels, supplementation of the solution/pH
control could have increased cell death and a decline in productivity.
Comparably, cultures supplemented with the osmolality control feed for
high nutrient conditions also showed about a 20\% drop in total cell
growth and productivity (p \textless{} 0.35). However, moderate and low
nutrient conditions supplemented with the osmolality feed control did
not show any significant differences from the control cultures
suggesting that the accumulation of additional osmolality by the
cultures in high nutrient conditions was an artefact of the already
nutrient rich environment and not of the control feed. Therefore, the
effects of osmolality and the pH change from the amino acid cocktail
feeds did not contribute to the overall increase in cell growth or
productivity, but it was in fact a result of the key amino acids
supplementation.

The growth and production models for Criterion 3 represented those
nutrients that were consumed less than their theoretical demand but were
not deemed important by the model VIP statistic. Presumably, these
nutrients were considered not to significantly impact cell growth or
productivity within all three nutrient conditions. Although day 9 CVC
was chosen as the response variable, relative cell growth rates from
Criterion 2 showed that the peak cell growth occurred prior to day 7.
This is further reflected in the experimental results for Criterion 3
growth model where there was insignificant change to total cells
measured in response to day 8 amino acid supplementation for all three
nutrient feed levels (Fig. 6a). Similarly, growth model conditions for
all three nutrient levels resulted in about a 20\% decrease in relative
titer when compared to the control (Fig. 6b). Overall, the production
model resulted in about a 5\% increase in total cells for high and
moderate nutrient conditions, and about a 15\% decrease in total cells
for the low nutrient conditions when compared to the control. Relative
titer on the other hand showed a 10\% increase for the high nutrient
condition (p \textless{} 0.3) and about a 40\% increase for both
moderate and low nutrient conditions (p \textless{} 0.05). Although 40\%
increase was presumed to be significant, it was not as significant as
the 90\% increase in the analogous cultures within Criterion 2 (p
\textless{} 0.001). We presume that the large increase in titer from
moderate and low nutrient feed conditions in Criterion 3 was due to the
low nutrient levels in the culture and that any additional nutrients
could provide a positive effect.

\emph{Driving Consumption of Amino Acids}

Although amino acid supplementation for the high nutrient condition had
minimal impact, the larger increases in cell growth and productivity
within Criterion 2 demonstrated an approach to identify limiting
nutrients in the moderate and low nutrient controls. However, to
determine if the limiting nutrients were indeed the model derived amino
acids, consumption rates were compared between model conditions and the
respective control within each nutrient feed level from Criterion 2
conditions (Fig. 8). The time dependent differences in amino acid
consumption rates between the process controls for each nutrient feed
level were represented as either a positive (green) difference
reflecting an increase in consumption or a negative (red) difference
reflecting a decrease in consumption (Fig. 7). For classification
purposes, the amino acids supplemented to the model-driven conditions
were highlighted and were grouped as either glucogenic or ketogenic.
Glucogenic amino acids can provide a carbon source to the cells to
biosynthesize glucose for metabolism whereas ketogenic amino acids
provide a carbon source to generate ketone bodies which can serve as a
secondary energy source in oxidative metabolism (Brosnan, 2003; Noguchi
et al., 2010).

Previously, it has been postulated that amino acid consumption is
largely dependent on the concentration of the corresponding amino acid
(Fan et al., 2015). Indeed, this was true for the high nutrient feed
conditions in which not only the model-supplemented amino acids, but
almost all amino acids showed an increase in consumption up to and
including day 11 for both models. The few with reduced consumption
included glutamic acid, which showed a marked decrease in consumption
across all time points after day 3. Although glutamic acid is a
nonessential amino acid for CHO cells, we posit that this decrease in
glutamic acid consumption is driven by a shift to increase consumption
of other supplemented nonessential amino acids, such as glycine and
alanine. However, due to the limited increase in cell growth and mAb
productivity from these conditions, overall increased consumption did
not shift the cells to a higher metabolic state, suggesting a saturation
state for cells and a point of maximum contribution by amino acids.

In contrast, moderate and low nutrient conditions showed a more drastic
difference in the consumption patterns when compared to the high
nutrient conditions. Most noticeably, there was a marked decrease in the
consumption of ketogenic amino acids and increased consumption of
glucogenic amino acids suggesting a greater need for energy and
biosynthesis due to the limited nutrient conditions. Furthermore, for
moderate nutrient conditions the growth model-derived amino acids had
increased consumption earlier in the culture and production
model-derived amino acids such as methionine were consumed more in the
latter half of the culture, supporting the distinct difference in
metabolic requirements between the cell growth phase and the high
mAb-producing stationary phase. In the low nutrient condition, there was
a decrease in majority of the amino acids within the growth model but
increase in glutamic acid and alanine in the latter half of the culture.
In the low nutrient production model, methionine and eventually lysine
showed increased consumption resulting in increased mAb productivity. In
all cases, model-derived amino acids were generally consumed more when
supplemented according to Criterion 2 than process control cultures for
each respective nutrient condition. Accordingly, these amino acids were
potential limiting nutrients that pushed cells into a higher metabolic
state when supplemented.

\textbf{Discussion}

Herein we present a novel approach to utilize amino acid stoichiometric
balances as inputs into MVDA models such as the orthogonal partial least
squares algorithm to balance key amino acids in chemically-defined cell
culture media supplements to increase CHO cell growth and productivity.
However, the utilization of stoichiometric balances in chemometric
approaches is not novel. Experimental stoichiometric models date as
early as 1994 where Xie and Wang designed a cell culture medium
development strategy in which the key nutrients required in biomass and
product generation could be described mathematically by stoichiometric
coefficients (Xie \& Wang, 1994b; Xie \& Wang, 1994c). Since increased
cell mass is a necessary requirement to produce the desired
concentration of key biologic products such as mAbs, the specific cell
growth rate (u\textsubscript{growth}) and specific productivity (qP)
become two key governing parameters within the stoichiometric equation.
The resulting stoichiometric balance would help derive the theoretical
demand of each nutrient, and thus, Xie and Wang showed that various
nutrients could be balanced within complex CD media without the
necessity of multi-factorial DoEs.

For instance, in a follow up study, Xie and Wang used their
stoichiometric model to decrease ammonia and lactate formation in
hybridoma cells by balancing the basal medium nutrient levels. In this
model, they analyzed the relationship between glutamine and nonessential
amino acids as a function of lactate and ammonia production rates. The
modified medium resulted in a 4-fold decrease in ammonia production and
almost a 10-fold decrease in lactate formation from the hybridoma cells
with the added benefit of increased cell growth and product formation
(Xie \& Wang, 1994a). Val et al utilized the stoichiometric model to
balance nucleotide sugars as a function of cell growth and specific
productivity to understand nucleotide sugar demand towards glycosylation
profiles in CHO cells (Del Val, Polizzi, \& Kontoravdi, 2016). Xie and
Nyberg et al further utilized the stoichiometric modeling approach in
CHO cells by designing a serum-free feed medium with balanced nutrients
to improve cell growth and IFNy productivity as well as glycosylation
efficiency for IFNy (Xie et al., 1997).

Similarly, we derived stoichiometric balances to improve cell growth and
productivity as a function of all 20 amino acids. In agreement with the
original method, the stoichiometric coefficients or theoretical demands
for amino acids derived in our model were based on their contributions
towards biomass and mAb productivity as a function of specific growth
rate (\selectlanguage{greek}µ\selectlanguage{english}\textsubscript{growth}) and specific productivity (qP).
Accordingly, Xie and Wang's original method also considered the cell
death rate, thus resulting in gross growth rate (Xie \& Wang, 1994c).
Cell death rate becomes particularly important during the
late-stationary and death phases of the CHO cell culture where viable
cell densities and viabilities start to decline (Balandras et al.,
2011). The increased death rate during the latter half of the culture is
attributed to several factors including increased concentration of
harmful byproducts such as NH3, increased packed cell volume, and rapid
nutrient elimination (Pan, Dalm, Wijffels, \& Martens, 2017b; Pascoe,
Arnott, Papoutsakis, Miller, \& Andersen, 2007). Death rates as a
result, are either calculated quantitatively by measuring differential
levels of extracellular LDH accumulation that is released from lysed or
apoptotic cells or theoretically by adjusting the net growth rate by a
factor correlating to viability decline (Mart\selectlanguage{ngerman}ínez, Bulté, Contreras,
Palomares, \& Ramírez, 2020; Martins Conde Pdo, Sauter, \& Pfau, 2016;
Templeton et al., 2017). Although the net growth rate was used in our
calculation for theoretical demand, the growth model only predicted
important variables up to day 9 in the culture at which point the
viabilities of the cultures were relatively similar suggesting minute
differences between gross and net growth rates. The resulting
stoichiometric balance solution was obtainable by taking the difference
between the empirical consumption and the theoretical demand of every
amino acid. In all cases however, the underlaying assumption behind
stoichiometric balances was that the intracellular metabolism and
complex gene expression machinery could be generalized into a ``black
box'' in which extracellular fluxes of nutrients from the media could be
directly related to biomass and product generation.

Statistical models in bioprocess have also relied on the ``black box''
approach in correlating extracellular metabolites and fluxes to cellular
phenotypical behavior (Kroll, Hofer, Ulonska, Kager, \& Herwig, 2017;
Lee \& Gilmore, 2006). In addition, multivariate approaches also offer
the added benefit of being able to highlight key variables that
contribute towards the prediction of specific response variables
(Akarachantachote et al., 2013; Gangadharan et al., 2019; Hassan,
Farhan, Mangayil, Huttunen, \& Aho, 2013). Applied together with the
stoichiometric model, the complexity of balancing all 20 amino acids in
CD media can be greatly reduced by balancing only the specific amino
acids deemed important by the statistical model. Furthermore,
statistical models are easier to develop, do not require systematic
constraints or curation of biological parameters, and are
computationally efficient in determining key correlations (Kim, Rocha,
\& Maia, 2018; Martins Conde Pdo et al., 2016). More recently however,
there has been keen interest on obtaining a deeper understanding of the
effects on the metabolic framework by stoichiometric balancing via
mechanistic modeling (Sha, Huang, Wang, \& Yoon, 2018). Such models can
elucidate the intricacies of the intracellular pathways that are
extrapolated within statistical models. Thus, mechanistic models can
help identify causal linkages within correlation structures. In a
modeling review, Traustason et al described several computational
methods aimed at optimizing amino acid concentrations for CD media in
CHO cell culture. Among them include stoichiometric models such as
metabolic flux analysis (MFA) or flux balance analysis (FBA) as well as
kinetic models (Traustason, B., Cheeks, \& Dikicioglu, 2019). Robitaille
et al developed a dynamic model combining the benefits of MFA and
kinetic models to explain the relationship between extracellular fluxes
of amino acids, extracellular concentrations, and the intracellular flux
responses towards that consumption. With a hybrid steady-state and
kinetic model, a dynamic relationship between nutrient uptake and
cellular response in terms of biomass generation and mAb production was
determined (Robitaille, Chen, \& Jolicoeur, 2015b).

In another example, combination of FBA and genome-scale modeling with
the utilization of amino acid stoichiometric balancing revealed that the
addition of nonessential amino acids (NEAAs) have a positive impact on
CHO cell biomass production (Traustason, Bergthor, 2019). CHO cells are
reported to contain seven NEAAs including glycine, alanine, asparagine,
aspartic acid, glutamic acid, proline, and serine (Fomina-Yadlin et al.,
2014). These seven amino acids are nutrients that CHO cells can directly
biosynthesize whereas the remaining 13 essential amino acids must be
obtained by nutrient supplementation from the CD media (Salazar et al.,
2016). Presumably, the supplementation of NEAAs can redirect the energy
needed from biosynthesis of amino acids to other biological processes
such as cell growth or protein synthesis. Moreover, several essential
amino acids are also used in biosynthesis for NEAAs and other metabolic
intermediates, suggesting that supplementation of NEAAs could not only
free up energy but also free up nutrients to support the biosynthesis of
other cellular processes (Duarte et al., 2014; Harcum \& Lee, 2016).
Accordingly, the significant increases of cell growth and mAb
productivity that were observed within moderate and low nutrient
conditions for both the growth and production models in Criterion 2
supported the energy conservation theory of NEAAs since two of the three
amino acids supplemented for cell growth were NEAAs. Supplementation of
alanine and glycine also showed increased consumption in all model
conditions which also resulted in a decreased specific consumption of
glucose further suggesting that the conserved energy was shifted towards
cell growth and increased cellular metabolism. In the case of mAb
productivity, methionine and lysine was also supplemented. Although not
counted within NEAAs, methionine plays an important role in protein
production as it is the universal initiator of protein synthesis and
thus, crucial to cellular uptake and metabolism to increase protein
production. In addition, methionine has shown to improve the cellular
redox state of cells by using the ubiquitous methionine sulfoxide cycle
to provide an antioxidant defense system (Lim, Kim, \& Levine, 2019).
Accordingly, we presume that the supplementation of NEAAs, critical
protein synthesis amino acids, and increased cell growth all contributed
towards the significant increase in mAb productivity within moderate and
low nutrient model conditions.

In the case of high nutrients feeds, although there was a marked
increase in cellular consumption of almost all amino acids, there was
only a minute increase in cell growth and mAb productivity, and we
presumed that a saturation point in the culture was reached. However,
the notion of a saturation point with respect to extracellular amino
acid concentrations was supported by Salazar et al who described that
supplementing concentrations of amino acids that are generally highly
consumed in mammalian cell cultivation does not always lead to
improvement in cell culture, but rather can lead to undesired effects
and the accumulation of harmful waste products (Salazar et al., 2016).
Similarly, Templeton et al experimentally validated previous MFA models
with \textsuperscript{13}C labeling studies \emph{in vitro} and showed
that protein expression does not always correspond the activation of
specific metabolic pathways, but rather, even fluxes tend to eventually
saturate (Templeton et al., 2017b). Taken together, high nutrient
conditions resulted in greater consumption but maintained similar
specific glucose consumption rates suggesting that cellular energy was
not repurposed to increased cell growth or mAb productivity, rather, the
cells had reached their maximum capacity to metabolize amino acids.

\textbf{Conclusion}

The methods presented in this study were consolidated as a single
platform approach to rapidly optimize amino acid concentrations as CD
media supplements (Fig. 8). Since amino acids are one of the most
important building blocks for cellular biomass and protein production,
they also comprise an essential component group in CD media. In
addition, since the relative amino acid requirement is similar across
CHO cell lines and similar between various mAbs, the amino acid modeling
platform presented here can be applied to various CHO cell cultures
expressing various mAbs (Széliová et al., 2020). Nevertheless, Xie and
Wang's original stoichiometric model was inclusive of all media
nutrients and thus, our empirical modeling approach and methods to
calculate stoichiometric balances could be generalized to other
nutrients as well, for example, vitamins, co-factors, trace elements,
organic, and inorganic salts among others. Although raw measurements of
nutrient concentrations can be directly input into MVDA approaches (Fig.
8 (1a)), calculation of secondary variables such as cell growth rate,
specific productivity, and consumption rates can help formulate
stoichiometric balances which in turn can serve as enhanced inputs to
derive causal linkages (Fig. 8 (1b-1c)). Within the modeling platform,
MVDA dimensional reduction algorithms such as PLS or OPLS can be
utilized to understand the correlation between the dynamics of
time-dependent stoichiometric balances and key response variables such
as cell growth or mAb productivity. VIP statistics and correlation
coefficients from multivariate algorithms can help generate importance
and directionality criteria for the input variables. Key nutrients
towards specific response variables or cellular phenotypical states can
be further translated into experimental designs for validation studies
(Fig. 8 (2a)). However, in the case of stoichiometric balances, a
feature selection decision tree approach can be implemented to choose
the appropriate stoichiometric balances for process developing. Bolded
here is the positive correlated balances that are negative in value
which potentially represent limiting nutrients as shown in Criterion 2
(Fig. 8 (2b-2c)). However, negatively correlated stoichiometric balances
could also be considered for media formulation development. To support
multivariate statistical models, experimental validation is necessary to
not only verify the performance of the model, but also measure the
success criteria of the desired phenotypical state. Model outputs can
dictate supplementation with modified nutrient feeds to be validated in
a targeted DoE, which in turn can generate new cell culture data to
refine against the MVDA model (Fig. 8 (3 -- 4)).

Since the prediction of the statistical model is largely based on the
variance of the training dataset, high variance datasets can provide a
larger prediction space for the model and a reduction in model bias.
However, models training on datasets with high variance rely heavily on
the upper and lower bounds of the variance space and thus, any
validation datasets that fall outside of the training dataset space can
lead to poor success. Therefore, as new processes are adapted based on
model-driven conditions, future datasets can be combined with training
datasets to iteratively improve the model (Fig. 8 (5)) (Luo et al.,
2020). For instance, important amino acid stoichiometric balances based
on high nutrient feeds were also fed to the moderate and low nutrient
conditions resulting in significant increases in cell growth and mAb
productivity. However, in future iterations the newly generated
validation datasets could help improve the original training dataset and
help increment towards an improved biologics production process and
optimized CD media.

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Figure Legends

\textbf{Fig. 1. Variance and distribution of training dataset:} A
25-batch CHO cell culture experiment was designed to obtain a training
dataset to test the amino acid stoichiometric balance MVDA model in
which the culture was supplemented with various amounts of high nutrient
feeds within a defined fed-batch process. Data on cell growth and mAb
titer from all batches was analyzed to obtain peak growth and
productivity time points and a PCA model was generated to analyze the
distribution and variance of training batches with respect to the amino
acid stoichiometric balances. (a) VCD peaked between day 6 to day 9
across the 25 training batches with a majority peaking near day 9 (Black
Lines). Similarly, CVC at each time point was also plotted along side
VCD to show a similar distribution (Green dashed lines). Cell growth
data up to day 9 represented the log-growth phase of the cell culture,
thus, day 9 CVC was chosen as the response variable for the growth
model. (b) Titer data was normalized to the peak titer value of the
fed-batch process control. Since mAb titer represented an accumulation
of extracellular secreted mAb in the spent media, peak titer occurred at
the end of the process on day 14. Accordingly, day 14 titer was chosen
as the response variable for the production model. (c). Distribution of
the batches based on principle components 1 and 2, which cumulatively
described 53.5\% of the variance did not show any significant grouping
or clustering of the batches thereby eliminating the possibility of any
inherent bias in the data. (d) Similarly, the loadings plot of the
time-dependent amino acid stoichiometric balances showed a wide
distribution without any collinearity of variables at specific time
points.

\textbf{Fig. 2. Criteria for Model-based Amino Acid Selection:} VIP
values and coefficients from the OPLS models along with stoichiometric
balance directionalities from the process control were utilized as
selection factors in 3 unique criteria for amino acids. (a-b) Criteria 1
amino acid SBs represented positive correlation to either Day 9 CVC or
Day 14 Titer, a VIP value greater than 1, and a positive stoichiometric
balance sign. (c-d) Criteria 2 amino acid SBs represented positive
correlation to either Day 9 CVC or Day 14 Titer, a VIP value greater
than 1, and a negative stoichiometric balance sign. (e-f) Criteria 3
amino acid SBs represented positive correlation to Day 9 CVC, a VIP
value less than 0.5, and a negative stoichiometric balance sign.
Coefficient values were normalized and scaled to unit variance by the
model, and only positively correlated amino acid SBs were selected.
Since time-dependent amino acid SBs were used in the model, various
selected time points that met each respective criterion were plotted.
For each model and criteria, amino acid cocktail feeds were developed
grouped by day of importance. For instance, in the growth model for
criteria 1 (a), Asp, Ser, Pro, and Val were highlighted as important on
Day 3, and thus, a cocktail of all 4 amino acids was developed and fed
on day 3 of the culture.

\textbf{Fig. 3. Criteria 1 Validation of Culture Performance with
respect too Cell Growth and mAb Productivity:} Amino acids for the
growth model (Day 9 CVC) and the Production model (Day 14 Titer) were
supplemented to CHO cell culture batches that ran with the high nutrient
fed-batch process according to the selection factors from criteria 1
(Corr \textgreater{} 1, VIP \textgreater{} 1, SB \textgreater{} 0). Day
9 and Day 14 values for CVC and Titer were normalized to the maximum
value of the process control (black). Error bars represent standard
error to mean. (a) Amino acids supplementation for models based on
criteria 1 did not result in a significant increase in total cells by
day 9. Only the growth model showed a nominal increase of
\textasciitilde{}10\% at day 14 when compared to control (p \textless{}
0.15). (b) Similarly, no significant increase of mAb productivity was
observed when compared to the process control for either model and in
the case of the growth model, mAb productivity decreased by
\textasciitilde{}20\% by day 14 (p \textless{} 0.05).

\textbf{Fig. 4. Criteria 2 Validation of Culture Performance with
respect too Cell Growth and mAb Productivity:} In addition to the high
nutrient fed-batch process, model informed amino acid supplements based
on criteria 2 (Corr \textgreater{} 1, VIP \textgreater{} 1, SB
\textless{} 0) were also tested on moderate and low nutrient fed-batch
processes. Accordingly, Day 9 and Day 14 values for CVC and Titer were
normalized to the maximum value of each respective process control (Gray
Line). Error bars represent standard error to mean. (Relative CVC) Amino
acids supplementation based on criteria 2 showed \textasciitilde{}20\%
increase in total cells for high nutrient, but close to a
\textasciitilde{}30\% increase in moderate nutrients conditions (p
\textless{} 0.05). The relative total cells was even more profound in
low nutrient reaching near \textasciitilde{}55\% increase in total cells
(p \textless{} 0.01). (Relative Titer) Antibody titer in contrast
increased only for the production model for high nutrient feeds but
drastically for both models in moderate and low nutrient feeds reaching
close to \textasciitilde{}80\% increase in titer by day 9 and a 60\%
increase in titer by day 14 with respect to each process control (p
\textless{} 0.001).

\textbf{Fig. 5. A comparison of total glucose consumption and specific
glucose consumption:} To determine if criteria 2 amino acid
supplementation for both, the growth and the production models modified
the metabolic state of the cells, the total glucose consumption of each
culture was compared to the specific glucose consumption per cell. The
total glucose consumption was calculated by the change in extracellular
glucose concentrations between feed events in the process. Specific
glucose consumption was calculated like total glucose consumption
however, the difference was divided by the change in CVC between each
time point. Although total glucose consumption showed a slight decrease
in moderate and low nutrient conditions, a more profound decrease was
noticed in the specific glucose consumption rates for moderate and low
nutrients feeds suggesting that cells under moderate and low nutrient
conditions shifted consumption for carbon source and energy from glucose
to other preferred metabolites such as the stoichiometrically balanced
amino acids.

\textbf{Fig. 6. Criteria 3 Validation of Culture Performance with
respect too Cell Growth and mAb Productivity:} To test the effectiveness
of the VIP value to select biologically important amino acids only,
amino acids were supplemented according to the selection factors from
criteria 3 (Corr \textgreater{} 1, VIP \textgreater{} 0.5, SB
\textless{} 0). Supplementation based on criteria 3 was assumed to
result in a minimal change in cell growth and mAb productivity for both
models (a) Accordingly, no significant change in D14 CVC was observed
across all nutrient conditions, with some cases resulting in a decrease
of cell growth. (b) In contrast, there was a significant in increase in
titer for both moderate and low nutrient conditions in the production
model (p \textless{} 0.05), presumably due to the lack of nutrient
levels in those conditions. However, this increase was not as
significant as supplementation with criteria 2 amino acids.

\textbf{Fig. 7. Driving consumption of model informed amino acids:} To
validate the statistical model, it was important to assess if the model
driven amino acid supplementations led to an increased consumption of
supplemented amino acids and/or activated the consumption of other amino
acids. Specific consumption rates were calculated from the change in
extracellular amino acid levels between feed events per cell. The
resulting specific consumption rates within model conditions were
compared to the consumption rates of the respective process control for
each nutrient level. Positive changes are reflected by green boxes and
negative by red. Gray boxes indicate missing values that were not
captured by amino acid assay for various reasons. In addition, amino
acids were grouped between glucogenic and ketogenic groups.

\textbf{Fig. 8. Media optimization platform with Stoichiometric
Balances:} The modeling approach presented in this study was a proof of
concept to utilize stoichiometric balances for amino acids to rapidly
optimize media development efforts. However, stoichiometric balances and
the methods presented could also be applied to other macro-nutrients
necessary in CD media. Accordingly, figure 8 presents our approach as a
platform to iteratively improve various stages of media development.
Utilization of MVDA can easily highlight key stoichiometric balances
that can be filtered through a feature selection decision tree to
identify the limiting nutrients. Experimental validation studies can
then be conducted to assess the change in phenotypical behavior with the
modified media. Lastly, the newly generated data can be combined with
the original dataset to further inform and improve media development
efforts.

Supplementary Figure Text

\textbf{Fig. S1. Training Model Statistics:} MVDA models using the
Orthogonal Partial Least Squares (OPLS) algorithm in SIMCA-P+ were
generated using 25 training batches. Models were built towards day 9 CVC
or day 14 titer in the batch level model format. In addition to the
goodness of fit (R\textsuperscript{2}) parameter, a goodness of
prediction (Q\textsuperscript{2}) parameter was also generated that
measured the cross-validated prediction accuracy. (a) Observed vs
predicted plot for day 9 CVC showed a strong R\textsuperscript{2} of
0.912, and a strong Q\textsuperscript{2} of 0.726. (b). Observed vs
predicted plot for day 14 titer showed a strong R\textsuperscript{2} of
0.832 but a predictable accuracy of 0.422. Although the
Q\textsuperscript{2} was relatively lower, the day 14 titer model was
able to highlight information on key variables for media optimization.

\textbf{Fig. S2. Criteria 2 Relative Growth Rate and Relative Specific
Productivity.} Relative growth rate for high nutrient condition showed a
slight increased by day 3 and maintained the increase by day 7 which
could explain the slight increase (\textasciitilde{}20\%) in total cells
for high nutrient feeds. Relative growth rates for moderate and low
nutrient feeds also showed only slight increases, however remained
slightly higher for a longer duration of time than the high nutrient
condition. As a result, there was a more significant increase in total
cells for moderate and low nutrient conditions. Similarly, relative
productivity (qP) showed a more profound increase in moderate and low
nutrient conditions. Moderate nutrient conditions showed a 20 increase
in qP for the growth model (p \textless{} 0.05) and showed near a 30\%
increase for the production model (p \textless{} 0.01). In contrast, the
low nutrient condition showed about a 40\% increase in qP starting from
day 7 (p \textless{} 0.05) suggesting the increased mAb production was
not only an artifact of increased cell growth, but a higher drive for
these cells to produce more monoclonal antibody.

\textbf{Fig. S3. Cell Growth and Productivity Changes resulting from
Process Controls:} Since amino acid cocktails were made at a 100x
concentration for each of the specific amino acids, increased pH by NaOH
was needed to solubilize the mixtures. In addition, highly concentrated
cocktail mixtures also resulted in a high osmolality. Therefore, to
measure the effects of high pH and high osmolality (osmo), a pH water
solution was generated at the highest pH among the amino acid cocktail
mixtures and fed to the cultures at the same volume as the cocktail
mixture. In addition, a high osmo solution in water was generated using
NaCl and fed at the same volume as the amino acid cocktail with the
highest osmo. pH controls were only measured against the high nutrient
conditions and resulted in a slight decrease of about 20\% in total
cells. Similarly, pH controls showed about a 30\% decrease in relative
titer. Osmo controls for high nutrient conditions showed similar trends
as the pH controls but showed minimal differences for moderate and low
nutrient conditions. The minimal overall effects of the pH control and
the osmo control on total cells and relative titer suggest that the
significant increases in cell growth and mAb production from criteria 2
cultures was attributed to the amino acids within the cocktail mixtures.\selectlanguage{english}
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