(199b) Towards Personalized Treatments for Leukemia Based on Cell Cycle Heterogeneity: An Experimental/Modeling Approach

Leukemia arises when blood cell progenitors experience
the wrong combination of genetic alterations; these heterogeneous clonal
changes induce reduced cell death and increased cell proliferation. Most
leukemia treatments focus on the simpler task of tumor debulking
rather than restoring normal cell function; this motivates our study of the
cell cycle.

A common type of chemotherapy treatment for highly
proliferative cells relies on cell cycle phase-specific (CCS) drugs. CCS drugs
selectively attack duplicating cells, by interfering with the processes carried
out in only one of the cell cycle phases. Importantly, CCS drugs affect not
only malignant cells but also normal cells in duplication; achieving a
trade-off between eradicating the tumor and maintaining a sufficient number of
healthy cells is crucial. However, clinical treatment protocols do not
incorporate this constraint in their calculations from the start of treatment;
instead, only factors that are believed to be related to drug tolerance are
taken into account (patient's weight, height, other diseases etc.). One of the biggest challenges in this area
is that of delivering truly personalized chemotherapy.

The heterogeneity of genetic modifications giving rise
to the disease is one of the main sources of variation in treatment response
between individual patients. One critical example of patient heterogeneity is
the average duration of each cell cycle phase, which can vary by hours or days
(Preisler et al., 1995). Biologically, not a single
population of leukemic cells but a variety of them is what characterizes a
tumor. Pefani et al. (2013, 2014) showed that cell cycle kinetics are one of
the most significant variables affecting treatment outcomes. Since both inter-
and intra- patient genetic heterogeneity are reflected in cell cycle kinetics,
and drug action takes place at the cell cycle phase level, we hypothesize that a mathematical model that describes cell
cycle kinetics for each single, homogeneous population can be useful in the
calculation of optimal chemotherapy protocols.

In this work, we present a multi-stage population
balance model of the cell cycle consisting of 3 compartments: lumped G0/G1
(quiescent/gap 1 phase); S (DNA synthesis phase); lumped G2/M (gap 2/mitosis phase).
Each compartment is distributed according to a relevant state variable: cyclin E (G0/G1), DNA (S) and cyclin
B (G2/M). Cyclins E and B are proteins that trigger
cell cycle progression events in G1 and G2 phases respectively, and DNA
duplicates in S phase. Cyclin and DNA production
rates are assumed to be constant and the transitions are modeled as normal
cumulative distribution functions. The model is discretized using a fully
stable upwind scheme; care is taken to maintain sufficient discretization
intervals to avoid loss of entities. Global sensitivity analysis was carried
out in MATLAB and identified the cell cycle times (duration of each of the
phases) as the most relevant variables for phase numbers, and cyclin thresholds (the average cyclin
level at which cells transition) for cyclin kinetics.

The experimental determination of these parameters is
presented for three different leukemic cell lines, derived from different types
of leukemia: K-562 (Chronic Myeloid); MEC-1 (Chronic Lymphoid); MOLT-4 (Acute
Lymphoblastic). The cell cycle times were obtained by following an EdU labeled population over time (EdU
resembles one of the DNA building blocks and can be incorporated selectively in
S phase cells only, resulting in both EdU positive
and negative populations) and identifying the timings of entrance and exit from
each cell cycle phase. The cyclin thresholds were
found when cells reached the end of a particular phase and normalized as in García-Münzer et al. (2013). The model was then run in gPROMS (Process Systems Enterprise) and plotted against the
experimental EdU negative cell cycle distribution
over time. The agreement amongst the
model prediction and the experimental data was extremely good for all three
cell lines (the Chi-square test indicated there is no statistical
difference between the model output and the experimental data). In parallel, the cyclin
expression trends were well captured, which is measurable proof that the model
is based on the same assumptions as the biological processes.

In order to validate the model independently and
moving towards capturing cellular heterogeneity in patients, blind co-culture
experiments were carried out. The purpose of the blind experiment was to prove
that the model could differentiate between cell types based on heterogeneity in
cell cycle kinetics. A second operator prepared an unknown mixture of 2 to 3 of
the aforementioned cell lines (different cell types and ratios), which was put
in culture. The cell cycle kinetics were recorded for
each population. The model was then run assuming all possible scenarios (any
combination of cell lines in 10% increment ratios), and the one presenting the
smallest statistical error to the experimental data in every population was
chosen. The model was capable of identifying
and quantifying heterogeneous cell populations according to their cell cycle
kinetics.

The development of more detailed models of the cell
cycle that are experimentally validated is critical in the implementation of
more advanced pharmacokinetic/pharmacodynamic models
(Velliou et al., 2014). Additionally, connecting a small subset of measurable
variables to individual characteristics is necessary for the personalization of
treatments. The work presented here helps bridging the gap between both.

References

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Pefani E., Panoskaltsis N., Mantalaris A.,
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Pefani E., Panoskaltsis N., Mantalaris A.,
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Velliou E., Fuentes-Garí M., Misener R., Pefani E., Rende
M., Panoskaltsis N., Pistikopoulos E. N., Mantalaris A. A framework for the design, modeling and optimization of biomedical systems.
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Acknowledgements

This
work is supported by ERC-BioBlood (no. 340719),
ERC-Mobile Project (no. 226462), by the EU 7th Framework Programme [MULTIMOD
Project FP7/2007-2013, no 238013] and by the Richard Thomas Leukaemia Research
Fund. R.M. is further thankful for a Royal Academy of Engineering Research
Fellowship.