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Phase transitions of biological phenotypes by means of a prototypical PDE model Cover

Phase transitions of biological phenotypes by means of a prototypical PDE model

By: C. Mascia,  P. Moschetta and  C. Simeoni  
Open Access
|Feb 2020

References

  1. 1. D. Yao, C. Dai and S. Peng, Mechanism of the Mesenchymal-Epithelial Transition and its relationship with metastatic tumor formation, Molecular Cancer Research, vol. 9, no. 12, pp. 1608–1620, 2011.
  2. 2. J.P. Thiery and J.P. Sleeman, Complex networks orchestrate epithelial-mesenchymal transitions, Nature Reviews Molecular Cell Biology, vol. 7, no. 2, pp. 131–142, 2006.10.1038/nrm1835
  3. 3. P.C. Davies, L. Demetrius and J.A. Tuszynki, Cancer as dynamical phase transition, Theoretical Biology and Medical Modelling, vol. 8, pp. 1–30, 2011.10.1186/1742-4682-8-30
  4. 4. M. Mojtahedi, A. Skupin, J. Zhou, I.G. Castaño, R.Y.Y. Leong-Quong, H. Chang, K. Trachana, A. Giuliani and S. Huang, Cell fate decision as high-dimensional critical state, PLOS Biology, vol. 14, no. 12, p. e2000640, 2016.10.1371/journal.pbio.2000640
  5. 5. J. Xu, S. Lamouille and R. Derynck, TGF-β-induced epithelial to mesenchymal transition, Cell Research, vol. 19, no. 2, pp. 156–172, 2009.10.1038/cr.2009.5
  6. 6. M. Bertolaso, Philosophy of cancer. A dynamic and relational view. History, Philosophy and Theory of the Life Sciences 18, Springer Science+Business Media Dordrecht, Springer Netherlands, 2016.
  7. 7. C. Simeoni, S. Dinicola, A. Cucina, C. Mascia and M. Bizzarri, Systems Biology approach and Mathematical Modeling for analyzing phase-space switch during Epithelial-Mesenchymal Transition, in Systems Biology (M. Bizzarri, ed.), Methods in Molecular Biology 1702, pp. 95–123, Springer Protocols+Business Media LLC, 2018.10.1007/978-1-4939-7456-6_7
  8. 8. M. Bizzarri, A. Cucina, F. Conti and F. D’Anselmi, Beyond the oncogene paradigm: understanding complexity in carcinogenesis, Acta Biotheoretica, vol. 56, no. 3, pp. 173–196, 2008.10.1007/s10441-008-9047-8
  9. 9. G. Barrière, P. Fici, G. Gallerani, F. Fabbri and M. Rigaud, Epithelial Mesenchymal Transition: a double-edged sword, Clinical and Translational Medicine, vol. 4, no. 14, pp. 1–6, 2015.10.1186/s40169-015-0055-4
  10. 10. M.W. Green and B.D. Sleeman, On FitzHugh’s nerve axon equations, Journal of Mathematical Biology, vol. 1, pp. 153–163, 1974.10.1007/BF00275800
  11. 11. M.A. Jones, B. Song and D.M. Thomas, Controling wound healing through debridement, Mathematical and Computer Modelling, vol. 40, pp. 1057–1064, 2004.
  12. 12. R. Gesztelyi, J. Zsuga, A. Kemeny-Beke, B. Varga, B. Juhasz and A. Tosaki, The Hill equation and the origin of quantitative pharmacology, Archive for History of Exact Sciences, vol. 66, pp. 427–438, 2012.10.1007/s00407-012-0098-5
  13. 13. J. Monod, J. Wyman and J.P. Changeux, On the nature of allosteric transitions: a plausible model, Journal of Molecular Biology, vol. 12, pp. 88–118, 1965.10.1016/S0022-2836(65)80285-6
  14. 14. J.N. Weiss, The Hill equation revisited: uses and misuses, The FASEB Journal, vol. 11, no. 11, pp. 835–841, 1997.10.1096/fasebj.11.11.9285481
  15. 15. R.I. Masel, Principles of adsorption and reaction on solid surfaces, Wiley Series in Chemical Engineering 3, John Wiley & Sons, 1996.
  16. 16. C.S. Holling, Some characteristics of simple types of predation and parasitism, The Canadian Entomologist, vol. 91, no. 7, pp. 385–398, 1959.10.4039/Ent91385-7
  17. 17. P.C. Fife and J.B. McLeod, The approach of solutions of nonlinear diffusion equations to travelling front solutions, Archive for Rational Mechanics and Analysis, vol. 65, pp. 335–361, 1977.10.1007/BF00250432
  18. 18. J.A. Sherratt and B.P. Marchant, Algebraic decay and variable speeds in wavefront solutions of a scalar reaction-diffusion equation, IMA Journal of Applied Mathematics, vol. 56, pp. 289–302, 1996.10.1093/imamat/56.2.289
  19. 19. A. Quarteroni, Numerical models for differential problems. Third edition. Modeling, Simulation and Applications 16, Springer, Cham, 2017.10.1007/978-3-319-49316-9
  20. 20. R.J. LeVeque and H.C. Yee, A study of numerical methods for hyperbolic conservation laws with sti source terms, Journal of Computational Physics, vol. 86, no. 1, pp. 187–210, 1990.10.1016/0021-9991(90)90097-K
  21. 21. C. Lattanzio, C. Mascia, R.G. Plaza and C. Simeoni, Kinetic schemes for assessing stability of traveling fronts for the Allen-Cahn equation with relaxation, Applied Numerical Mathematics, vol. 141, pp. 234–247, 2019.10.1016/j.apnum.2018.10.009
  22. 22. P. Moschetta and C. Simeoni, Numerical investigation of the Gatenby-Gawlinski model for acid-mediated tumour invasion, Rendiconti di Matematica e delle sue Applicazioni, pp. 1–31, online first, 2019.
  23. 23. R.J. LeVeque, Finite difference methods for ordinary and partial differential equations. Steady-state and time-dependent problems. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2007.10.1137/1.9780898717839
  24. 24. B.H. Gilding and R. Kersner, Travelling waves in nonlinear diffusion-convection reaction. Progress in Nonlinear Differential Equations and Their Applications 60, Springer Basel AG, 2004.10.1007/978-3-0348-7964-4
Language: English
Page range: 1 - 17
Submitted on: Sep 12, 2018
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Accepted on: Nov 13, 2019
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Published on: Feb 1, 2020
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year

© 2020 C. Mascia, P. Moschetta, C. Simeoni, published by Italian Society for Applied and Industrial Mathemathics
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.