B. Alberts, A. Johnson, J. Lewis, M. Raff, K. Roberts et al., Molecular Biology of the Cell. Garland Science, 2007.

A. Arnold, P. Markowich, G. Toscani, and A. Unterreiter, On convex sobolev inequalities and the rate of convergence to equilibrium for Fokker-Planck type equations, Communications in Partial Differential Equations, vol.26, issue.1-2, pp.43-100, 2001.

M. Bagnat and K. Simons, Cell surface polarization during yeast mating, Proceedings of the National Academy of Sciences, vol.99, issue.22, pp.14183-14188, 2002.

P. Biler, G. Karch, P. Laurençot, and T. Nadzieja, The 8?-problem for radially symmetric solutions of a chemotaxis model in the plane, Mathematical Methods in the Applied Sciences, vol.29, issue.13, pp.1563-1583, 2006.

A. Blanchet, On the parabolic-elliptic Patlak-Keller-Segel system in dimension 2 and higher. Séminaire Laurent Schwartz -EDP et applications, pp.2011-2012
URL : https://hal.archives-ouvertes.fr/hal-00620500

J. María, . Cáceres, A. José, B. Carrillo, and . Perthame, Analysis of nonlinear noisy integrate & fire neuron models: blow-up and steady states, The Journal of Mathematical Neuroscience, vol.1, issue.1, p.7, 2011.

J. María, R. Cáceres, and . Schneider, Blow-up, steady states and long time behaviour of excitatory-inhibitory nonlinear neuron models, Kinetic & Related Models, vol.10, issue.3, 2017.

V. Calvez, R. Hawkins, N. Meunier, and R. Voituriez, Analysis of a nonlocal model for spontaneous cell polarization, SIAM Journal on Applied Mathematics, vol.72, issue.2, pp.594-622, 2012.

V. Calvez, N. Meunier, and R. Voituriez, A one-dimensional Keller-Segel equation with a drift issued from the boundary, C. R. Math. Acad. Sci, vol.348, pp.629-634, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00424649

A. José, M. Carrillo, M. P. González, M. E. Gualdani, and . Schonbek, Classical solutions for a nonlinear fokkerplanck equation arising in computational neuroscience, Communications in Partial Differential Equations, vol.38, issue.3, pp.385-409, 2013.

A. José, B. Carrillo, D. Perthame, D. Salort, and . Smets, Qualitative properties of solutions for the noisy integrate and fire model in computational neuroscience, Nonlinearity, vol.28, issue.9, p.3365, 2015.

W. Chen, Q. Nie, T. Yi, and C. Chou, Modelling of yeast mating reveals robustness strategies for cell-cell interactions, PLoS Computational Biology, vol.12, issue.7, 2016.

C. Chou, L. Bardwell, Q. Nie, and T. Yi, Noise filtering tradeoffs in spatial gradient sensing and cell polarization response, BMC Systems Biology, vol.5, issue.1, p.196, 2011.

C. Chou, Q. Nie, and T. Yi, Modeling robustness tradeoffs in yeast cell polarization induced by spatial gradients, PLoS ONE, vol.3, p.3103, 2008.

I. Csiszár, Information-type measures of difference of probability distributions and indirect observations, Studia Sci. Math. Hungar, vol.2, pp.299-318, 1967.

G. Dumont, J. Henry, and C. O. Tarniceriu, Noisy threshold in neuronal models: connections with the noisy leaky integrate-and-fire model, Journal of Mathematical Biology, vol.73, issue.6, pp.1413-1436, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01414588

M. Jayme, N. S. Dyer, M. Savage, . Jin, R. Trevin et al., Tracking shallow chemical gradients by actin-driven wandering of the polarization site, Current biology, vol.23, issue.1, pp.32-41, 2013.

L. C. Evans, Partial differential equations, Graduate Studies in Mathematics, vol.19, 2010.

T. Freisinger, B. Klünder, J. Johnson, N. Müller, G. Pichler et al., Establishment of a robust single axis of cell polarity by coupling multiple positive feedback loops, Nature communications, vol.4, p.1807, 2013.

H. Gajewski, On a variant of monotonicity and its application to differential equations, Nonlinear Analysis: Theory, Methods & Applications, vol.22, pp.73-80, 1994.

R. Hawkins, O. Bénichou, M. Piel, and R. Voituriez, Rebuilding cytoskeleton roads: active transport induced polarisation of cells, Phys. Rev., E, vol.80, p.40903, 2009.

C. L. Jackson and L. H. Hartwell, Courtship in s. cerevisiae: both cell types choose mating partners by responding to the strongest pheromone signal, Cell, vol.63, issue.5, pp.1039-1051, 1990.

M. Jin, B. Errede, M. Behar, W. Mather, S. Nayak et al., Yeast dynamically modify their environment to achieve better mating efficiency, Science Signaling, vol.4, issue.186, pp.54-54, 2011.

I. Kim and Y. Yao, The Patlak-Keller-Segel model and its variations: Properties of solutions via maximum principle, SIAM Journal on Mathematical Analysis, vol.44, issue.2, pp.568-602, 2012.

S. Kullback, On the convergence of discrimination information, IEEE Trans. Information Theory, IT, vol.14, pp.765-766, 1968.

M. J. Lawson, B. Drawert, M. Khammash, L. Petzold, and T. Yi, Spatial stochastic dynamics enable robust cell polarization, PLoS Comput Biol, vol.9, issue.7, p.1003139, 2013.

A. T. Layton, N. S. Savage, A. S. Howell, Y. Susheela, D. G. Carroll et al., Modeling Vesicle Traffic Reveals Unexpected Consequences for Cdc42p-Mediated Polarity Establishment, Current Biology, vol.21, issue.3, pp.184-194, 2011.

T. Lepoutre, N. Meunier, and N. Muller, Cell polarisation model: the 1D case, J. Math. Pures Appl, vol.101, issue.9, pp.152-171, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00776613

K. Madden and M. Snyder, Cell polarity and morphogenesis in budding yeast, Annual Review of Microbiology, vol.52, issue.1, pp.687-744, 1998.

C. Travis-i-moore, Q. Chou, N. Nie, T. Li-jeon, and . Yi, Robust spatial sensing of mating pheromone gradients by yeast cells, PLoS ONE, vol.3, p.3865, 2008.

H. Travis-i-moore, H. Tanaka, N. Kim, T. Li-jeon, and . Yi, Yeast G-proteins mediate directional sensing and polarization behaviors in response to changes in pheromone gradient direction, Molecular Biology of the Cell, vol.24, issue.4, pp.521-555, 2013.

N. Muller, M. Piel, V. Calvez, R. Voituriez, J. Gonçalves-sá et al., A predictive model for yeast cell polarization in pheromone gradients, PLoS Computational Biology, vol.12, issue.4, p.1004795, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01334085

S. Natasha, A. T. Savage, D. Layton, and . Lew, Mechanistic mathematical model of polarity in yeast, Molecular biology of the cell, vol.23, issue.10, pp.1998-2013, 2012.

M. Simon, C. D. Virgilio, B. Souza, A. John-r-pringle, S. Abo et al., Role for the rho-family gtpase cdc42 in yeast mating-pheromone signal pathway, Nature, vol.376, issue.6542, pp.702-705, 1995.

D. Brian, S. E. Slaughter, R. Smith, and . Li, Symmetry breaking in the life cycle of the budding yeast, Cold Spring Harbor perspectives in biology, vol.1, issue.3, 2009.

D. Brian, . Slaughter, A. Jay-r-unruh, S. E. Das, B. Smith et al., Non-uniform membrane diffusion enables steady-state cell polarization via vesicular trafficking, Nature communications, vol.4, p.1380, 2013.

C. Villani, Topics in optimal transportation, Graduate Studies in Mathematics, vol.58, 2003.

R. Wedlich-soldner, S. Altschuler, L. Wu, and R. Li, Spontaneous cell polarization through actomyosin-based delivery of the cdc42 gtpase, Science, vol.299, issue.5610, pp.1231-1235, 2003.

R. Wedlich-soldner, S. C. Wai, T. Schmidt, and R. Li, Robust cell polarity is a dynamic state established by coupling transport and gtpase signaling, The Journal of cell biology, vol.166, issue.6, pp.889-900, 2004.