Preprint, 11th IFAC Symposium on Dynamics and Control of Process Systems,
including Biosystems
June 6-8, 2016. NTNU, Trondheim, Norway
In Silico Cell Cycle Predictor for Mammalian Cell Culture Bioreactor Using
Agent-Based Modeling Approach
Elif S. Bayrak1, Tony Wang1, Matt Jerums1, Myra Coufal1, Chetan Goudar1, Ali Cinar2, Cenk Undey1
1
Amgen, Inc., Process Development, One Amgen Center Drive, Thousand Oaks, CA 91320 USA
(Tel: 805-447-0955; e-mail: [email protected], [email protected], [email protected], [email protected],
[email protected], [email protected]).
2
Department of Chemical and Biological Engineering, Illinois Institute of Technology, 10W 33rd St, Chicago, IL, 60616 USA
(e-mail: [email protected])}
Abstract: An Agent-based computational modeling approach was used to develop a model to simulate
individual mammalian cell behavior and its cycle regulation in response to dynamic bioreactor conditions.
The model can be used as an in silico cell cycle predictor when provided with data from ongoing bioreactor
runs. Rules were developed to regulate the distinct cell cycle events as well as to apply decision-making at
the critical cellular checkpoints. The model was constructed and validated using different sets of
experimental cell culture conditions with cell culture parameters measured using a flow cytometer and other
instrumentation.
Keywords: CHO cells, Agent-based modeling, cell cycle, mammalian cell culture
Typically, the flow cytometer has been the standard tool to
obtain cell cycle data on cultured cells (Davey and Kell,
1996). This off-line approach is expensive and requires
substantial sample handling and analysis time that makes it
impractical for monitoring and control of cell culture,
especially in a manufacturing environment. To overcome
these limitations, an automated flow cytometer was
developed to analyse culture heterogeneity over time (AbuAbsi et al., 2003), and it was used to predict approach of
stationary phase for successful scale-up operations (Sitton
and Srienc, 2008). While this technique is more automated it
still requires capital investment, setup and maintenance.
1. INTRODUCTION
Consistent high product quality at low cost is one of the most
desired, yet challenging outcomes in the biopharmaceutical
industry. Many complexities and variation are involved in
each unit operation related to the cell line development, the
culture medium formulations, process raw materials and
culture scale up and purification processes. There has been a
tremendous amount of research that focuses on maximizing
productivity of mammalian cells that produce therapeutic
proteins. High phenotypic heterogeneity is observed during
cell culture due to the varying progression in cell cycle,
imperfect mixing, and genetic variation. Robust
determination of cell cycle distribution in mammalian cell
culture processes is thus critical and can be directly translated
to knowledge to improve productivity of the culture.
Development of a mathematical model of cell cycle can
provide real time cell physiological state prediction and
improve understanding of the relationships between cell
cycle, medium composition, and culture condition which can
be used to optimize cell culture productivity and product
quality. One of the most common modelling approaches for
cell cycle modelling to capture heterogeneity is the
population-balance approach where a number of groups are
distinguished and represented as a variable corresponding to
their number or density and the temporal relationship
between these variables is defined mathematically (García
Münzer et al., 2015, Mantzaris et al., 2001). Agent-based
modeling (ABM) approach is more focused on the individual
behaviour and considered as a natural way to model such
systems comprised of heterogeneous individual entities
(Bonabeau, 2002). ABM is a novel, powerful simulation
paradigm that can facilitate combining qualitative and
quantitative information, while accounting for system
stochasticity. The number of studies benefiting from ABM’s
ease of modelling biological phenomena has been increasing
While there is no consensus in the literature on phasic
dependency of the protein expression, as it is likely related to
differences in cell lines and processes, the importance of cell
cycle knowledge is well recognised. Higher specific antibody
production was observed when the cells were arrested at G1/S
phase (al-Rubeai and Emery, 1990), while another study
showed higher productivity of interferon-γ was related to S
phase (Leelavatcharamas et al., 1999). Availability of such
knowledge can also facilitate many important process-related
decision-makings such as scale-up (Sitton and Srienc, 2008),
temperature shift or feed timing. Real-time cell cycle and
apoptosis data can lead to significant improvement in
monitoring and control strategies for bioreactors in
biopharmaceutical industries focusing on Process Analytical
Technology (PAT) applications (Kuystermans et al., 2014).
Copyright © 2016 IFAC
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June 6-8, 2016. NTNU, Trondheim, Norway
in the last decade (Bayrak et al., 2014, Mehdizadeh et al., An
and Christley, 2011, Bayrak et al., 2015a).
The cell cycle is a set of periodic events each cell will
experience before successful division with distinct sequential
phases such as G1 (Gap 1), S (DNA synthesis), G2 (Gap 2)
and M (mitosis) (Fig.2). Cell-cycle progression was simply
defined as “clock + checkpoint”, since it has clock-like
periodicity and switch-like ‘check-points’ where a yes-or-no
decision is made about the next event (Aghaeepour et al.,
2013).
In this work, experimentally obtained cell cycle data for
Chinese Hamster Ovary (CHO) cell culture using an off-line
flow cytometer were analysed and used to build a rule-based
relation between cell culture parameters and cell cycle
progression. Part of the rule base for this model is adopted
from our previous study to simulate individual mammalian
cell behavior in response to dynamic bioreactor conditions in
a fed-batch bioreactor (Bayrak et al., 2015b). This model has
been extended to study the effects of temperature (T) and pH
in addition to other cell culture variables. The model focuses
on predicting cell cycle behaviour of individual cells by
incorporating cell culture variables as inputs from the
relevant experimental study.
The rules are derived from the literature and data analysis
based on the experimental study. Environmental conditions
are defined based on the relative concentration of selected
bioreactor variables (Bayrak et al., 2015). The abstracted rule
base is shown in Fig.3. Each CHO agent receives the
environmental conditions based on that and its state (i.e., cell
cycle phase) in the previous time step, then decides either to
go through the cell cycle or apoptosis path. During this step,
the cell also updates its parameter set governing its behavior.
Complete rule-base and parameters have been described
previously (Bayrak et al., 2015).
2. METHODS
2.1 Agent-Based Modeling Approach
An agent-based model is developed to simulate individual
mammalian cell (CHO cell) behavior and its cell cycle
regulation in response to dynamic cell culture conditions. An
agent is defined as a software entity that makes decisions
based on environmental input and its internal machinery. In
order to describe cell cycle progression in the bioreactor,
naturally, a CHO cell is defined as the primary agent. The
model only focuses on the cellular biological level and
describes the cell cycle phase switch based on important
bioreactor environmental variables that are defined as
bioreactor temperature (T), pH, dissolved oxygen (DO),
glucose, lactate and sodium concentration (Fig.1). Partial
least squares (PLS) analysis is performed to decide model
variables (results are not reported). The CHO Agent model
takes the measurements of these variables from the real
process as environmental input, predicts cell cycle
distribution (G0/G1, S, G2/M) along with early apoptotic
(EA), late apoptotic (LA) and necrotic (N) cell distribution.
Figure 2. Cell cycle phases and check points
In the cell cycle rule-base, each agent has an embedded cycle
clock to track the time they spent in the current cycle phase.
When this clock reaches the maximum time it can spend in
the current phase, the cells will automatically go through the
checkpoints to see if environmental conditions allow
proceeding to the next phase. G1 or G2 arrest may occur due
to damage in DNA (Freeman, 2000), however it was not
accounted for in the model. G2 and M phase have been
combined to one state called G2M for convenience. Cells can
only proliferate at the end of the G2M phase if they satisfy the
conditions and both daughter cells will start the cell cycle
from G1 phase. A cell may also experience quiescent phase,
G0, where it will be dormant and not go through the cell
cycle. When the environmental conditions are severe such as,
high toxin accumulation, low DO and low nutrients, a cell
may abort the cycle and enter the apoptotic pathway. Early
apoptosis might be reversible state, and a cell might go back
to the cell cycle pathway if environmental conditions
improve, while late apoptosis is an irreversible state that will
lead to final necrosis.
Figure 1. Information flow for the CHO cell agent
The model is implemented in Java and uses Repast
(REcursive Porous Agent Simulation Toolkit), which is a
Java-based open source agent modeling toolkit (North et al.,
2013, Barnes and Chu, 2015). The model is developed in 3D,
however no spatial dependence was introduced in this work.
Necrosis probability is defined based on the shear sensitivity
of cells under different environmental conditions and cell
cycle phase. Higher probability of necrosis is assigned to
cells in their G0 and G1 phase since they are more sensitive to
shear than cells in S and G2M phase (Lakhotia et al., 1992).
2.2 CHO Cell Rule-Base
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June 6-8, 2016. NTNU, Trondheim, Norway
Figure 3. CHO cell agent rule base
Low temperature and high pH are observed to decrease the
shear sensitivity and low necrosis probability is assigned to
these conditions (Ludwig et al., 1992, Petersen et al., 1988).
Certain conditions such as sudden temperature drop or pH
may result in cell arrest the G0G1 or G2M phase (Moore et al.,
1997)
Table 1. Model parameters for CHO cell agent
The agent population is comprised of a non-interacting
heterogeneous population. Each agent has a random
distribution of parameters and different history (cell cycle
phase, cell age, etc.), which when initialized, makes the cell
respond to the same environmental stimuli in a different way.
Doubling time (total time to cycle) of a CHO cell is
calculated from the experimental data and the time spent in
each cell cycle phase is adopted from the literature. ABM
was tuned to find the best parameter set within the
physiological range for parameters to match the experimental
observations. Parameters governing the CHO cell cycle are
listed in Table 1.
2.3 Experimental Study
A proprietary Amgen recombinant CHO cell line and
chemically defined mammalian cell culture media was used
in this study.
Experiments were performed in a 3L bioreactor with 1.5 L
working volume. Millipore guava easyCyte 5HTTM flow
cytometer with guava ViaCountTM was used for cell density
and viability measurements. MultiCaspaseTM for caspase
activity-late apoptosis, NexinTM for annexin binding-early
apoptosis and Cell CycleTM assays were performed. FlowJo
version 10 (FLOWJO LLC) was used to fit the cell cycle
populations. Glucose, lactate, and sodium measurements
were performed using Nova Biomedical FLEX an average of
three times a day.
Behavior Parameter
ABM value
Doubling time (td)
19-28 hours
G1 phase time
%40 td
S phase time
%35 td
G2M phase time
%25 td
GLC lower limit
0.0014 g/L107 cells
O2 survival limit
%10
Max. time to spend on EA
21 hr
Max. time to spend on LA
12 hr
Lactate upper limit
3 g/L
Lactate lower limit
0.5 g/L
Na+ upper limit
100 mM
Necrosis probability
(Variable)
•
•
•
•
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Increase if environment
is severe
Increase if cell state is
G1 or G0
Decrease if T drop or
pH increases
Increase if pH
decreases
IFAC DYCOPS-CAB, 2016
June 6-8, 2016. NTNU, Trondheim, Norway
Three sets of experiments were conducted to evaluate the
impact of pH and T change on cell cycle distribution and
culture viability (Table 2).
In experiment 3, both T and pH was shifted down after the
critical VCD was achieved. Sudden pH drop might result
with higher shear sensitivity of cells (Petersen et al., 1988).
This case resulted with lowest viable cell density. Since pH
shift was performed through CO2 addition, there might some
adverse impact on cell metabolism and health coming from
high pCO2 that was not explicitly modelled. While model
predictions after T shift for S and G2M phase was good, the
sudden drop in G0G1 later in the culture was not captured
well by the model.
Table 2. Design of experiments
Exp.
Number
1
2
3
Initial T
Initial pH
T shift
pH Shift
37°C
37°C
37°C
6.9
6.9
6.9
33°C
30°C
33°C
6.9
7.2
6.6
3. RESULTS
An agent-based model was developed to simulate cases
defined in Table 2 to predict cell cycle progression in a cell
culture bioreactor. Experiment 1 data were used to train the
model and experiment 2 and 3 were used to validate the
model. The model is initialized using the corresponding data
point (t=0) from the experiments.
There are two stages in the process separated by T shift at
critical time (tc): Proliferation (before T-shift) and Production
(after T-shift). In experiment 1, bioreactor pH was kept
constant and T was shifted after a critical cell density was
achieved. Simulated cell states were collected at each time
step and compared with cell cycle phase data collected from
experiments and analysed in the flow cytometer. In Fig. 4
comparison of VCD between experimental and simulation
results were illustrated for the three experiments. Model
showed good agreement with experimentally measured VCD
for all cases. For experiment 1 and 3, model prediction was
higher than the experimental findings before (tc) for a short
period of time. Better agreement for VCD was observed after
T shift for all cases.
Comparison of experimental and simulation results for cell
cycle phases (G0G1, S, G2M) are illustrated in Fig. 5.
In experiment 1, pH was kept constant and T was shifted
after a critical cell density was achieved. Until the T shift, a
cyclic behavior in model prediction is observed due to rapid
proliferation. After the temperature shift, there was sudden
decrease in S phase, suggesting that committed cells
completed their time in S phase and passed to G2M phase.
Later in the culture, decrease in G1 phase was observed
suggesting that it might be due to the higher shear sensitivity
of cells in this phase. The model captured the important
changes in the dynamics of cell cycle distribution.
In experiment 2, T was shifted further down to 30°C where as
pH was shifted up to 7.2. Similar trends were observed after
the critical time. The number of cells in G2M phase was
slightly less than experiment 1. Lower T might reduce the
metabolic activities of cell and caused disruption in cell
proliferation. Lower cell viability and viable cell density is
observed in this experiment. Model predictions showed good
agreement with the experimental data.
Figure 4. Comparison of VCD simulation predictions with
experimental results A) Experiment 1, B) Experiment 2,
C) Experiment 3
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June 6-8, 2016. NTNU, Trondheim, Norway
critical for process understanding and optimization, while use
of this model for online predictions offers numerous benefits.
An agent-based approach was used in this work to predict
cell cycle progression of CHO cells. The model is a pure
rule-base model where simple rules were derived from the
literature to simulate cell cycle behaviour of individual cell as
a response to important bioreactor parameters. One of the
biggest advantages of using agent-based modeling is
capturing the environmental heterogeneity and its influences
on individual agents. This work did not incorporate transport
equations to account for spatial gradients due to the well
mixed nature of the lab-scale of bioreactor of interest (3 L
with 2L working volume).
The model focused solely on the prediction of cell cycle
phases of cells, prediction of important nutrient and
metabolite concentration were not studied. These data were
directly fed to the model from experimental study.
Alternatively, coupling with first principle models could be
used to provide these inputs to the cycle model.
Until the T shift, a cyclic behavior in model prediction is
observed due to rapid proliferation. Cyclic behavior was not
captured in the experimental data. Better growth specific
markers and a more optimized predictive model may be
required to truly capture the cellular behaviour. Performing
separate experiments for each condition and more frequent
data collection from replicate experiments can also help
diagnose this inconsistency.
Cell cycle parameters such as the time to spend in each phase
are assumed to be insensitive to environmental conditions
apart from the checkpoints. However, duration of different
phases may vary given the environmental conditions, which
could be incorporated into the model to give better
predictions.
The model developed here was used to simulate a cell cycle
distribution in a mammalian cell culture bioreactor with a
focus on individual cell behaviour to changing environmental
conditions. The relationship between the cell cycle and
protein expression is not integrated in this model, however,
understanding this relationship is crucial for effective
operation of mammalian cell culture processes.
5. CONCLUSIONS
Figure 5. Comparison of simulation and experimental
results for cell cycle phase prediction
We have demonstrated that ABM can be used to predict
important dynamics of cell physiology such as cell cycle. The
model results were in good agreement with experimental data
suggesting utility of the ABM framework to describe cell
culture processes. Simulation predictions can lead to
significant process understanding and improvement in
monitoring and control strategies for cell culture process
thereby enabling more robust process development and
optimization.
4. DISCUSSION
Cell cycle distribution in cell culture bioreactors during the
production of important biologics is a critical piece of
knowledge to evaluate the health of the culture (Lloyd et al.,
1999). Properly developed mathematical relationships
between cell cycle progression and culture condition are
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