Mathematical Biosciences and Engineering, 2015, 12(5): 965-981. doi: 10.3934/mbe.2015.12.965.

Primary: 92D10, 65C99, 92-08, 92C45.

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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"

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.
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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. Mathematical Biosciences and Engineering, 2015, 12(5): 965-981. doi: 10.3934/mbe.2015.12.965

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  • 2. Margherita Carletti, Malay Banerjee, A Backward Technique for Demographic Noise in Biological Ordinary Differential Equation Models, Mathematics, 2019, 7, 12, 1204, 10.3390/math7121204

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Copyright Info: 2015, Margherita Carletti, et al., licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

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