Stochastic modelling of PTEN regulation in brain tumors: A model for glioblastoma multiforme

Margherita  Carletti; Matteo  Montani; Valentina  Meschini; Marzia  Bianchi; Lucia  Radici; Margherita  Carletti; Matteo  Montani; Valentina  Meschini; Marzia  Bianchi; Lucia  Radici

doi:10.3934/mbe.2015.12.965

Mathematical Biosciences and Engineering

2015, Volume 12, Issue 5: 965-981. doi: 10.3934/mbe.2015.12.965

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Stochastic modelling of PTEN regulation in brain tumors: A model for glioblastoma multiforme

1.
Department DISBEF, University of Urbino "Carlo Bo"
2.
Department DISBEF, University of Urbino "Carlo Bo", and Gran Sasso Science Institute
3.
Department DISB, University of Urbino "Carlo Bo"

Received: 01 October 2014 Accepted: 29 June 2018 Published: 01 June 2015
MSC : Primary: 92D10, 65C99, 92-08, 92C45.

This work is the outcome of the partnership between the mathematical group of Department DISBEF and the biochemical group of Department DISB of the University of Urbino "Carlo Bo" in order to better understand some crucial aspects of brain cancer oncogenesis.Throughout our collaboration we discovered that biochemists are mainly attracted to the instantaneous behaviour of the whole cell, while mathematicians are mostly interested in the evolution along time of small and different parts of it. This collaboration has thus been very challenging. Starting from [23,24,25], we introduce a competitive stochastic model for post-transcriptional regulation of PTEN, including interactions with the miRNA and concurrent genes. Our model also covers protein formation and the backward mechanism going from the protein back to the miRNA.The numerical simulations show that the model reproduces the expected dynamics of normal glial cells. Moreover, the introduction of translational and transcriptional delays offers some interesting insights for the PTEN low expression as observed in brain tumor cells.

Keywords:

Brain tumors,
gene regulation,
glioblastoma multiforme,
stochastic modelling,
PTEN,
numerical methods for genetic regulatory networks.

Citation: Margherita Carletti, Matteo Montani, Valentina Meschini, Marzia Bianchi, Lucia Radici. Stochastic modelling of PTEN regulation in brain tumors: A model for glioblastoma multiforme[J]. Mathematical Biosciences and Engineering, 2015, 12(5): 965-981. doi: 10.3934/mbe.2015.12.965

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Abstract

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