American Institute of Mathematical Sciences

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

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

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

Received  October 2014 Revised  April 2015 Published  June 2015

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.
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 & Engineering, 2015, 12 (5) : 965-981. doi: 10.3934/mbe.2015.12.965
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References:
 [1] William Chad Young, Adrian E. Raftery, Ka Yee Yeung. A posterior probability approach for gene regulatory network inference in genetic perturbation data. Mathematical Biosciences & Engineering, 2016, 13 (6) : 1241-1251. doi: 10.3934/mbe.2016041 [2] Giacomo Albi, Lorenzo Pareschi, Mattia Zanella. Opinion dynamics over complex networks: Kinetic modelling and numerical methods. Kinetic & Related Models, 2017, 10 (1) : 1-32. doi: 10.3934/krm.2017001 [3] Roberto Serra, Marco Villani, Alex Graudenzi, Annamaria Colacci, Stuart A. Kauffman. The simulation of gene knock-out in scale-free random Boolean models of genetic networks. Networks & Heterogeneous Media, 2008, 3 (2) : 333-343. doi: 10.3934/nhm.2008.3.333 [4] Jesse Berwald, Marian Gidea. Critical transitions in a model of a genetic regulatory system. Mathematical Biosciences & Engineering, 2014, 11 (4) : 723-740. doi: 10.3934/mbe.2014.11.723 [5] Kristin R. Swanson, Ellsworth C. Alvord, Jr, J. D. Murray. Dynamics of a model for brain tumors reveals a small window for therapeutic intervention. Discrete & Continuous Dynamical Systems - B, 2004, 4 (1) : 289-295. doi: 10.3934/dcdsb.2004.4.289 [6] Somkid Intep, Desmond J. Higham. Zero, one and two-switch models of gene regulation. Discrete & Continuous Dynamical Systems - B, 2010, 14 (2) : 495-513. doi: 10.3934/dcdsb.2010.14.495 [7] Xu Zhang, Xiang Li. Modeling and identification of dynamical system with Genetic Regulation in batch fermentation of glycerol. Numerical Algebra, Control & Optimization, 2015, 5 (4) : 393-403. doi: 10.3934/naco.2015.5.393 [8] Ö. Uğur, G. W. Weber. Optimization and dynamics of gene-environment networks with intervals. Journal of Industrial & Management Optimization, 2007, 3 (2) : 357-379. doi: 10.3934/jimo.2007.3.357 [9] Erik Kropat, Gerhard-Wilhelm Weber, Erfan Babaee Tirkolaee. Foundations of semialgebraic gene-environment networks. Journal of Dynamics & Games, 2020, 7 (4) : 253-268. doi: 10.3934/jdg.2020018 [10] Lijin Wang, Pengjun Wang, Yanzhao Cao. Numerical methods preserving multiple Hamiltonians for stochastic Poisson systems. Discrete & Continuous Dynamical Systems - S, 2021  doi: 10.3934/dcdss.2021095 [11] Qi Wang, Lifang Huang, Kunwen Wen, Jianshe Yu. The mean and noise of stochastic gene transcription with cell division. Mathematical Biosciences & Engineering, 2018, 15 (5) : 1255-1270. doi: 10.3934/mbe.2018058 [12] Mahdi Jalili. EEG-based functional brain networks: Hemispheric differences in males and females. Networks & Heterogeneous Media, 2015, 10 (1) : 223-232. doi: 10.3934/nhm.2015.10.223 [13] Ingenuin Gasser, Marcus Kraft. Modelling and simulation of fires in tunnel networks. Networks & Heterogeneous Media, 2008, 3 (4) : 691-707. doi: 10.3934/nhm.2008.3.691 [14] Kunwen Wen, Lifang Huang, Qiuying Li, Qi Wang, Jianshe Yu. The mean and noise of FPT modulated by promoter architecture in gene networks. Discrete & Continuous Dynamical Systems - S, 2019, 12 (7) : 2177-2194. doi: 10.3934/dcdss.2019140 [15] Qi Yang, Lei Wang, Enmin Feng, Hongchao Yin, Zhilong Xiu. Identification and robustness analysis of nonlinear hybrid dynamical system of genetic regulation in continuous culture. Journal of Industrial & Management Optimization, 2020, 16 (2) : 579-599. doi: 10.3934/jimo.2018168 [16] Joachim Escher, Anca-Voichita Matioc. Well-posedness and stability analysis for a moving boundary problem modelling the growth of nonnecrotic tumors. Discrete & Continuous Dynamical Systems - B, 2011, 15 (3) : 573-596. doi: 10.3934/dcdsb.2011.15.573 [17] Junde Wu, Shangbin Cui. Asymptotic behavior of solutions of a free boundary problem modelling the growth of tumors with Stokes equations. Discrete & Continuous Dynamical Systems, 2009, 24 (2) : 625-651. doi: 10.3934/dcds.2009.24.625 [18] Raffaele D'Ambrosio, Martina Moccaldi, Beatrice Paternoster. Numerical preservation of long-term dynamics by stochastic two-step methods. Discrete & Continuous Dynamical Systems - B, 2018, 23 (7) : 2763-2773. doi: 10.3934/dcdsb.2018105 [19] Xiaobing Feng, Shu Ma. Stable numerical methods for a stochastic nonlinear Schrödinger equation with linear multiplicative noise. Discrete & Continuous Dynamical Systems - S, 2021  doi: 10.3934/dcdss.2021071 [20] Raffaele D'Ambrosio, Stefano Di Giovacchino. Numerical preservation issues in stochastic dynamical systems by $\vartheta$-methods. Journal of Computational Dynamics, 2021  doi: 10.3934/jcd.2021023

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