A stochastic model for immunotherapy of cancer
Authored by Martina Baar, Loren Coquille, Hannah Mayer, Michael Hoelzel, Meri Rogava, Thomas Tueting, Anton Bovier
Date Published: 2016
DOI: 10.1038/srep24169
Sponsors:
German Research Foundation (Deutsche Forschungsgemeinschaft, DFG)
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Abstract
We propose an extension of a standard stochastic individual-based model
in population dynamics which broadens the range of biological
applications. Our primary motivation is modelling of immunotherapy of
malignant tumours. In this context the different actors, T-cells, cytokines or cancer cells, are modelled as single particles
(individuals) in the stochastic system. The main expansions of the model
are distinguishing cancer cells by phenotype and genotype, including
environment-dependent phenotypic plasticity that does not affect the
genotype, taking into account the effects of therapy and introducing a
competition term which lowers the reproduction rate of an individual in
addition to the usual term that increases its death rate. We illustrate
the new setup by using it to model various phenomena arising in
immunotherapy. Our aim is twofold: on the one hand, we show that the
interplay of genetic mutations and phenotypic switches on different
timescales as well as the occurrence of metastability phenomena raise
new mathematical challenges. On the other hand, we argue why
understanding purely stochastic events (which cannot be obtained with
deterministic models) may help to understand the resistance of tumours
to therapeutic approaches and may have non-trivial consequences on
tumour treatment protocols. This is supported through numerical
simulations.
Tags
Dynamics
Melanoma
Cells
Clonal evolution
Resistance
Therapy
Galton-watson processes
Moment equations
Limit
theorems
Tumor