P. Bayley, S. Schilstra, and . Martin, A simple formulation of microtubuie dynamics: quantitative implications of the dynamic instability of microtubule populations in vivo and in vitro, Journal of Cell Science, vol.93, pp.241-254, 1989.

A. Desai and T. Mitchison, MICROTUBULE POLYMERIZATION DYNAMICS, Annual Review of Cell and Developmental Biology, vol.13, issue.1, pp.83-117, 1997.
DOI : 10.1146/annurev.cellbio.13.1.83

M. Dogterom and S. Leibler, Physical aspects of the growth and regulation of microtubule structures, Physical Review Letters, vol.42, issue.9, pp.1347-1350, 1993.
DOI : 10.1103/PhysRevA.42.3637

H. Flyvbjerg, S. Holy, and . Leibler, Microtubule dynamics: Caps, catastrophes, and coupled hydrolysis, Physical Review E, vol.267, issue.5, pp.5538-5560, 1996.
DOI : 10.1002/cm.970100305

M. Greer, L. Pujo-menjouet, and G. Webb, A mathematical analysis of the dynamics of prion proliferation, Journal of Theoretical Biology, vol.242, issue.3, pp.598-606, 2006.
DOI : 10.1016/j.jtbi.2006.04.010

T. Hill and Y. Chen, Phase changes at the end of a microtubule with a GTP cap., Proceedings of the National Academy of Sciences, vol.81, issue.18, pp.815772-5776, 2002.
DOI : 10.1073/pnas.81.18.5772

P. Hinow, J. Rezania, and . Tuszynski, Continuous model for microtubule dynamics with catastrophe, rescue, and nucleation processes, Physical Review E, vol.12, issue.3
DOI : 10.1038/ncb1703

URL : http://arxiv.org/pdf/0811.2245

M. Kirschner and K. Mitchison, Dynamic instability of microtubule growth, Nature, vol.312, pp.237-242, 1984.

P. Laurençot and C. Walker, Well-posedness for a model of prion proliferation dynamics, Journal of Evolution Equations, vol.7, issue.2, pp.241-264, 2007.
DOI : 10.1007/s00028-006-0279-2

I. Maly, Diffusion Approximation of the Stochastic Process of Microtubule Assembly, Bulletin of Mathematical Biology, vol.64, issue.2, pp.213-238, 2002.
DOI : 10.1006/bulm.2001.0265

G. Margolin, . Gregoretti, . Cickovski, . Li, . Shi et al., The mechanisms of microtubule catastrophe and rescue: implications from analysis of a dimer-scale computational model, Molecular Biology of the Cell, vol.23, issue.4, 2012.
DOI : 10.1091/mbc.E11-08-0688

G. Margolin, . Gregoretti, M. Goodson, and . Alber, Analysis of a measoscopic stochastic model of microtubule dynamic instability, Physical Review E, vol.74, 2006.

E. Mukhtar, M. Adhami, and H. Mukhtar, Targeting Microtubules by Natural Agents for Cancer Therapy, Molecular Cancer Therapeutics, vol.13, issue.2, pp.275-284, 2014.
DOI : 10.1158/1535-7163.MCT-13-0791

URL : http://mct.aacrjournals.org/content/molcanther/13/2/275.full.pdf

A. Pagano, . Honoré, . Mohan, A. Berges, and . Akhmanova, Epothilone B inhibits migration of glioblastoma cells by inducing microtubule catastrophes and affecting EB1 accumulation at microtubule plus ends, Biochemical Pharmacology, vol.84, issue.4, pp.432-443, 2012.
DOI : 10.1016/j.bcp.2012.05.010

B. Perthame, Transport equations in biology, Frontiers in Mathematics, 2007.

B. Perthame, Parabolic equations in biology Lecture Notes on Mathematical Modelling in the Life Sciences

D. Sept, . Limbach, J. Bolterauer, and . Tuszynski, A Chemical Kinetics Model for Microtubule Oscillations, Journal of Theoretical Biology, vol.197, issue.1, pp.77-88, 1999.
DOI : 10.1006/jtbi.1998.0861

G. Simonett and C. Walker, On the solvability of a mathematical model for prion proliferation, Journal of Mathematical Analysis and Applications, vol.324, issue.1, pp.580-603, 2006.
DOI : 10.1016/j.jmaa.2005.12.036

R. Wade, On and Around Microtubules: An Overview, Molecular Biotechnology, vol.27, issue.Suppl 5, pp.177-191, 2009.
DOI : 10.1016/j.ceb.2007.11.005

C. Walker, Prion proliferation with unbounded polymerization rates, Proceedings of the Sixth Mississippi State?UBA Conference on Differential Equations and Computational Simulations, pp.387-397, 2007.

R. Walker, E. O-'brien, . Pryer, . Soboeiro, . Voter et al., Dynamic instability of individual microtubules analyzed by video light microscopy: rate constants and transition frequencies, The Journal of Cell Biology, vol.107, issue.4, pp.1437-1448, 1988.
DOI : 10.1083/jcb.107.4.1437

D. White, S. Hubert, and . Honoré, Exploring the effect of end-binding proteins and microtubule targeting chemotherapy drugs on microtubule dynamic instability, Journal of Theoretical Biology, vol.429, pp.18-34, 2017.
DOI : 10.1016/j.jtbi.2017.06.014

URL : https://hal.archives-ouvertes.fr/hal-01585717

E. Zauderer, Partial Differential Equations of Applied Mathematics, 2006.
DOI : 10.1002/9781118033302

J. Zhou and P. Giannakakou, Targeting Microtubules for Cancer Chemotherapy, Current Medicinal Chemistry-Anti-Cancer Agents, vol.5, issue.1, pp.65-71, 2005.
DOI : 10.2174/1568011053352569