Mathematical Modelling of Apoptosis for GS-NS0 Cell Culture Secreting Monoclonal Antibody: Linking Gene to Growth, Metabolism and Metabolic Stress

Mammalian cell culture systems
are widely utilised for bio-manufacturing, including the production monoclonal
antibodies (mAbs). Recently, mAbs
became ones of the pharmaceuticals of great importance due to their
capabilities to efficiently treat chronic diseases, such as cancers [1]. Up to 30 mAbs are successfully commercialised with the sale value of
18.5 billion dollars in 2010, which is also expected to be continuously
increasing within the next years [1, 2]. This fact reflects a steadily
constant rise in global demand for mAbs over the last
decade and attracts attention in bioprocess intensification for the production
of mAbs by mammalian cell culture systems. Several
approaches have been introduced to large scale mammalian cell culture systems
to meet the demand for mAbs: genetic engineering,
medium optimisation and manipulation of extracellular conditions. Nevertheless,
mAb production is subject to metabolic stress, and in
particular nutrient deficiency and toxic metabolite accumulation, which
normally occur as a result of cellular metabolism. The stresses have
detrimental impact on cell proliferation and favour cell death, thus reducing mAb titre. Therefore, intensifying mAb
secretion is still a challenging mission since there is much room for relieving
metabolic stress and ultimately increasing mAb final
titre.    

Attempts have been made in order
to enable cells to tolerate metabolic stress, resulting in a
longer culture viability and ultimately a higher mAb
production. Previously, apoptosis, or programmed cell death, was found to be a
main cause of cell death in the culture [3], and it is believed to be triggered
by metabolic stresses, especially nutrient deprivation [4, 5]. Cell lines with transfection of
anti-apoptotic gene(s), such as bcl-2 and bcl-x_L
exhibit resistance to apoptosis, consequently leading to a
prolonged culture viability [6, 7]. However, the extension of culture
viability lifespan does not always result in an increase in mAb
secretion [7, 8]. Cell
cycle arrest at G₁/G₀ phase was also found to be where mAb productivity was enhanced and has an intricate relation
to apoptosis. Transfection of p21 inducing cell proliferation arrest at
G₁/G₀ transition phases of the cell cycle shows promise
for enhancing mAb secretion; several fold increase in
mAb production was obtained by the culture of NS0
cell line with p21 over-expression [9]. Though cell cycle arrest at G₁/G₀
phase was also found to coexist with bcl-2 and bcl-x_L
over-expression [10], no significant rise in mAb production is often acquired by the culture of cell
lines with bcl-2 or bcl-x_L
transfection. These contradictory data together with the high complexity of
cellular systems emphasises the need for a systematic approach in order not to
focus only on a specific point of view, but to rather take into account a
complete picture of the problem/system. Therefore, a complete map of
interactions between/among cell proliferation, cell metabolism and apoptosis
(cell death) is needed in order to design an efficient strategy for achieving a
higher mAb production.    

Previously, we conducted a batch
culture study of GS-NS0 producing cB72.3 mAb to
reveal the culture profiles from the genetic level to extracellular metabolic
conditions. More specifically, an interplay map between cell cycle and
apoptosis at a transcriptional level, and their links to extracellular
metabolites, including glucose, glutamate, ammonium and lactate was introduced
[11]. The map
was enhanced with extracellular amino acid profiles, consequently revealing
amino acid deprivation effects on cell proliferation inhibition and the induction
of apoptosis. These data show strong connections between amino acid
deprivation, especially glutamate and aspartate, to the induction of apoptosis.
The sudden increase in atf5, casp8 and casp3 expression
suggests that cells initially die via the extrinsic pathway of apoptosis as a
response to the amino acid deprivation. The observed extracellular amino acid
profiles also suggest metabolic pathway adaptation as a result of amino acid
deprivation. For example, the production of alanine during the exponential
phase and the production of ammonium could point out a metabolic shift caused
by glutamate and aspartate deprivation [12].

In order to take into account a
complete picture of the observed experimental data, we propose here a
systematic framework (Figure 1) to build a mathematical model toward
model-based optimisation. This model was experimentally validated based on our
previous data. The model aims to capture apoptosis at a genetic level and its
link to cell growth, cell metabolism and extracellular nutrient and metabolite
profiles, and aims to incorporate observed features from the experimental data.
Our mathematical model was constructed based on the batch data

with fair balance between biological
information and model complexity. It can be divided into three main parts; cell
growth, cell metabolism and apoptosis, which is a combination of unstructured
and structured sub-models. The sub-model for cell growth and metabolism parts
was adopted from previously introduced adapted Monod kinetics, an unstructured
mathematical model linking cell growth to substrate utilisation, including
glucose and key amino acids, and the production of toxic metabolites: ammonium
and lactate [13-15].
The apoptosis sub-model was inspired by Koutinas, M.
et al. (2011) and aims to account for transcriptional and translational
regulation of apoptosis and links to growth and metabolism kinetics as a death
factor induced by metabolic stresses [16]. Parameter estimation was performed
to gain parameter values as regards the batch data. Global sensitivity analysis
(GSA) was employed to the model in order to identify sensitive parameters to
model outputs and reduce unnecessary model complexity. Our model shows a good
fit to the batch experimental data. Our preliminary GSA also confirms state
variables, such as viable cells and apoptotic cells, is dependent on their
parameters relating to these state variables, such as Monod constants for
glucose, glutamate and caspase3. The model is validated with an independent
experiment of fed-batch culture which is designed based on the batch
experimental data. The model refinement can be then considered at this stage.
In the future, Model-based optimisation will be applied to the finalised model
for suggesting feeding strategies. An experimental validation with the
suggested feeding schemes will be performed and might guide the direction in
the final model modification and significant parameter re-estimation. The
advantages of this approach over others are the less expensive cost from
experimental trial and possible error. This approach can be a basis for
improvement of bio-manufacturing applications, especially mammalian cell
culture systems producing recombinant proteins and antibodies.

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