M. Abkarian, G. Massiera, L. Berry, M. Roques, and C. Braun-breton, A novel mechanism for egress of malarial parasites from red blood cells, Blood, vol.117, issue.15, pp.24-34, 2011.
DOI : 10.1182/blood-2010-08-299883
URL : https://hal.archives-ouvertes.fr/hal-00630757

B. Audoly and S. Neukirch, Fragmentation of Rods by Cascading Cracks: Why Spaghetti Does Not Break in Half, Physical Review Letters, vol.95, issue.9, pp.95505-61, 2005.
DOI : 10.1103/PhysRevLett.95.095505

T. Blisnick, M. Betoulle, M. Barale, J. Uzureau, P. Berry et al., Pfsbp1, a Maurer's cleft Plasmodium falciparum protein, is associated with the erythrocyte skeleton, Molecular and Biochemical Parasitology, vol.111, issue.1, pp.107-131, 2000.
DOI : 10.1016/S0166-6851(00)00301-7

T. Blisnick, B. Morales, E. Maria, J. Barale, P. Uzureau et al., Pfsbp 1, a Maurer's cleft Plasmodium falciparum protein, is associated with the erythrocyte skeleton, p.17, 2000.

J. Boussinesq, Application des potentiels à l'étude de l'équilibre et du mouvement des solides élastiques (Gauthier-Villars, pp.1885-61

F. Brochard-wyart, P. De-gennes, and O. Sandre, Transient pores in stretched vesicles: role of leak-out, Physica A: Statistical Mechanics and its Applications, vol.278, issue.1-2, pp.32-45, 2000.
DOI : 10.1016/S0378-4371(99)00559-2

P. Buchak, C. Eloy, and P. Reis, The Clapping Book: Wind-Driven Oscillations in a Stack of Elastic Sheets, Physical Review Letters, vol.105, issue.19, pp.194301-194346, 2010.
DOI : 10.1103/PhysRevLett.105.194301
URL : https://hal.archives-ouvertes.fr/hal-00712231

A. Callan-jones, P. Brun, and B. Audoly, Self-Similar Curling of a Naturally Curved Elastica, Physical Review Letters, vol.108, issue.17, p.174302, 2012.
DOI : 10.1103/PhysRevLett.108.174302

A. Callan-jones, P. Brun, and B. Audoly, Self-Similar Curling of a Naturally Curved Elastica, Physical Review Letters, vol.108, issue.17, pp.174302-70, 2012.
DOI : 10.1103/PhysRevLett.108.174302

R. Chandramohanadas, P. Davis, D. Beiting, M. Harbut, C. Darling et al., Apicomplexan Parasites Co-Opt Host Calpains to Facilitate Their Escape from Infected Cells, Science, vol.324, issue.5928, pp.794-811, 2009.
DOI : 10.1126/science.1171085

R. Chandramohanadas, Y. Park, L. Lui, A. Li, D. Quinn et al., Biophysics of Malarial Parasite Exit from Infected Erythrocytes, PLoS ONE, vol.24, issue.13, pp.20869-20886, 2011.
DOI : 10.1371/journal.pone.0020869.s003

E. Chater and J. Hutchinson, On the Propagation of Bulges and Buckles, Journal of Applied Mechanics, vol.51, issue.2, pp.269-61, 1984.
DOI : 10.1115/1.3167611

A. Cho, NANOTECHNOLOGY: Pretty as You Please, Curling Films Turn Themselves Into Nanodevices, Science, vol.313, issue.5784, p.71, 2006.
DOI : 10.1126/science.313.5784.164

P. Cicuta, S. Keller, and S. Veatch, Diffusion of Liquid Domains in Lipid Bilayer Membranes, The Journal of Physical Chemistry B, vol.111, issue.13, pp.3328-3341, 2007.
DOI : 10.1021/jp0702088

B. Cooke, N. Mohandas, and R. Coppel, Malaria and the red blood cell membrane, Seminars in Hematology, vol.41, issue.2, pp.173-197, 2004.
DOI : 10.1053/j.seminhematol.2004.01.004

S. Dhawan, M. Dua, A. Chishti, and M. Hanspal, Ankyrin Peptide Blocks Falcipain-2-mediated Malaria Parasite Release from Red Blood Cells, Journal of Biological Chemistry, vol.278, issue.32, pp.30180-30197, 2003.
DOI : 10.1074/jbc.M305132200

R. Dimova, S. Aranda, N. Bezlyepkina, V. Nikolov, K. Riske et al., A practical guide to giant vesicles. Probing the membrane nanoregime via optical microscopy, Journal of Physics: Condensed Matter, vol.18, issue.28, pp.1151-1164, 2006.
DOI : 10.1088/0953-8984/18/28/S04

R. Dimova, C. Dietrich, A. Hadjiisky, K. Danov, and B. Pouligny, Falling ball viscosimetry of giant vesicle membranes: Finite-size effects, The European Physical Journal B, vol.12, issue.4, pp.589-602, 1999.
DOI : 10.1007/s100510051042

R. Dimova, C. Dietrich, A. Hadjiisky, K. Danov, and B. Pouligny, Falling ball viscosimetry of giant vesicle membranes: Finite-size effects, The European Physical Journal B, vol.12, issue.4, pp.589-625, 1999.
DOI : 10.1007/s100510051042

D. Discher and A. Eisenberg, Polymer Vesicles, Science, vol.297, issue.5583, 2002.
DOI : 10.1126/science.1074972

J. Dvorak, L. Miller, W. Whitehouse, and T. Shiroishi, Invasion of erythrocytes by malaria merozoites, Science, vol.187, issue.4178, p.748, 1975.
DOI : 10.1126/science.803712

E. Evans and W. Rawicz, Elasticity of ``Fuzzy'' Biomembranes, Physical Review Letters, vol.79, issue.12, pp.2379-2396, 1997.
DOI : 10.1103/PhysRevLett.79.2379

E. Evans and R. Skalak, Mechanics and Thermodynamics of Biomembranes, Journal of Biomechanical Engineering, vol.102, issue.4, p.16, 1980.
DOI : 10.1115/1.3138234

Y. Forterre, J. Skotheim, J. Dumais, and L. Mahadevan, How the Venus flytrap snaps, Nature, vol.185, issue.7024, p.421, 2005.
DOI : 10.1046/j.1365-313X.2001.01350.x
URL : https://hal.archives-ouvertes.fr/hal-01432204

S. Gerbode, J. Puzey, A. Mccormick, and L. Mahadevan, How the Cucumber Tendril Coils and Overwinds, Science, vol.337, issue.6098, p.1087, 2012.
DOI : 10.1126/science.1223304

P. Gilson and B. Crabb, Morphology and kinetics of the three distinct phases of red blood cell invasion by Plasmodium falciparum merozoites, International Journal for Parasitology, vol.39, issue.1, p.91, 2009.
DOI : 10.1016/j.ijpara.2008.09.007

S. Glushakova, G. Humphrey, E. Leikina, A. Balaban, J. Miller et al., New Stages in the Program of Malaria Parasite Egress Imaged in Normal and Sickle Erythrocytes, Current Biology, vol.20, issue.12, p.1117, 2010.
DOI : 10.1016/j.cub.2010.04.051

S. Glushakova, D. Yin, T. Li, and J. Zimmerberg, Membrane Transformation during Malaria Parasite Release from Human Red Blood Cells, Current Biology, vol.15, issue.18, pp.1645-1664, 2005.
DOI : 10.1016/j.cub.2005.07.067

G. Gupta and G. Mishra, Transbilayer phospholipid asymmetry in Plasmodium knowlesi-infected host cell membrane, Science, vol.212, issue.4498, pp.1047-1064, 1981.
DOI : 10.1126/science.7233198

V. Heinrich, K. Ritchie, N. Mohandas, and E. Evans, Elastic Thickness Compressibilty of the Red Cell Membrane, Biophysical Journal, vol.81, issue.3, pp.1452-1466, 2001.
DOI : 10.1016/S0006-3495(01)75800-6

V. Heinrich, K. Ritchie, N. Mohandas, and E. Evans, Elastic Thickness Compressibilty of the Red Cell Membrane, Biophysical Journal, vol.81, issue.3, pp.1452-1486, 2001.
DOI : 10.1016/S0006-3495(01)75800-6

S. Henon, G. Lenormand, A. Richert, and F. Gallet, A New Determination of the Shear Modulus of the Human Erythrocyte Membrane Using Optical Tweezers, Biophysical Journal, vol.76, issue.2
DOI : 10.1016/S0006-3495(99)77279-6

R. Hochmuth, P. Worthy, and E. Evans, Red cell extensional recovery and the determination of membrane viscosity, Biophysical Journal, vol.26, issue.1, pp.101-137, 1979.
DOI : 10.1016/S0006-3495(79)85238-8

M. Hu, S. Marrink, and M. Deserno, Gaussian curvature elasticity determined from global shape transformations and local stress distributions: a comparative study using the MARTINI model, Faraday Discuss., vol.86, pp.365-381, 2013.
DOI : 10.1039/C2FD20087B

J. Hutchinson and K. Neale, Neck propagation, Journal of the Mechanics and Physics of Solids, vol.31, issue.5, pp.405-61, 1983.
DOI : 10.1016/0022-5096(83)90007-8

H. W. Krenn and H. W. , Feeding Mechanisms of Adult Lepidoptera: Structure, Function, and Evolution of the Mouthparts, Annual Review of Entomology, vol.55, issue.1, p.307, 2010.
DOI : 10.1146/annurev-ento-112408-085338

W. Hwang and R. Waugh, Energy of dissociation of lipid bilayer from the membrane skeleton of red blood cells, Biophysical Journal, vol.72, issue.6, pp.2669-2685, 1997.
DOI : 10.1016/S0006-3495(97)78910-0

D. Kabaso, R. Shlomovitz, T. Auth, V. Lew, and N. Gov, Curling and Local Shape Changes of Red Blood Cell Membranes Driven by Cytoskeletal Reorganization, Biophysical Journal, vol.99, issue.3
DOI : 10.1016/j.bpj.2010.04.067

E. Karatekin, O. Sandre, H. Guitouni, N. Borghi, P. Puech et al., Cascades of Transient Pores in Giant Vesicles: Line Tension and Transport, Biophysical Journal, vol.84, issue.3, pp.1734-1753, 2003.
DOI : 10.1016/S0006-3495(03)74981-9
URL : https://hal.archives-ouvertes.fr/hal-00168676

S. Kyriakides, Propagating Instabilities in Structures, Adv. Appl. Mech, vol.30, pp.67-61, 1994.
DOI : 10.1016/S0065-2156(08)70174-1

L. Landau, Theory of elasticity, p.52, 1886.

L. Landau and E. Lifshitz, Theory of Elasticity, p.40, 1987.

M. Lanzer, H. Wickert, G. Krohne, L. Vincensini, and C. Braun-breton, Maurer's clefts: A novel multi-functional organelle in the cytoplasm of Plasmodium falciparum-infected erythrocytes, International Journal for Parasitology, vol.36, issue.1, pp.23-40, 2006.
DOI : 10.1016/j.ijpara.2005.10.001

M. Lanzer, H. Wickert, G. Krohne, L. Vincensini, and C. Breton, Maurer's clefts: A novel multi-functional organelle in the cytoplasm of Plasmodium falciparum-infected erythrocytes, International Journal for Parasitology, vol.36, issue.1, pp.23-24, 2006.
DOI : 10.1016/j.ijpara.2005.10.001

A. Love, A treatise on the mathematical theory of elasticity, ADDRESS, p.40, 2013.
URL : https://hal.archives-ouvertes.fr/hal-01307751

E. Mabrouk, D. Cuvelier, F. Brochard-wyart, P. Nassoy, and M. Li, Bursting of sensitive polymersomes induced by curling, Proc. Natl. Acad. Sci. USA, p.80, 2009.
DOI : 10.1073/pnas.0813157106
URL : https://hal.archives-ouvertes.fr/hal-01002414

E. Mabrouk, D. Cuvelier, F. Brochard-wyart, P. Nassoy, and M. Li, Bursting of sensitive polymersomes induced by curling, Proc. Natl. Acad. Sci. USA, pp.7294-7329, 2009.
DOI : 10.1073/pnas.0813157106
URL : https://hal.archives-ouvertes.fr/hal-01002414

A. G. Maier, B. Cooke, A. Cowman, and L. Tilley, Malaria parasite proteins that remodel the host erythrocyte, Nature Reviews Microbiology, vol.64, issue.5, pp.341-359, 2009.
DOI : 10.1038/nrmicro2110

E. Mandelkow, E. Mandelkow, and R. Milligan, Microtubule dynamics and microtubule caps: a time-resolved cryo- electron microscopy study, The Journal of Cell Biology, vol.114, issue.5, pp.977-980, 1991.
DOI : 10.1083/jcb.114.5.977

A. Merlen and C. Frankiewicz, Cylinder rolling on a wall at low Reynolds numbers, Journal of Fluid Mechanics, vol.10, pp.461-494, 2011.
DOI : 10.1007/s10404-007-0193-0
URL : https://hal.archives-ouvertes.fr/hal-00639831

L. Miao, B. Fourcade, M. Rao, M. Wortis, and R. Zia, Equilibrium budding and vesiculation in the curvature model of fluid lipid vesicles, Physical Review A, vol.43, issue.12, pp.6843-85, 1991.
DOI : 10.1103/PhysRevA.43.6843

J. P. Mills, M. Diez-silva, D. J. Quinn, M. Dao, M. J. Lang et al., Effect of plasmodial RESA protein on deformability of human red blood cells harboring Plasmodium falciparum, Proceedings of the National Academy of Sciences, vol.104, issue.22, pp.9213-9231, 2007.
DOI : 10.1073/pnas.0703433104

J. Mills, L. Qie, M. Dao, K. Tan, C. Lim et al., Continuous forcedisplacement relationships for the human red blood cell at different erythrocytic developmental stages of Plasmodium falciparum malaria parasite, MRS Proceedings, pp.7-8, 2004.

N. Mohandas and E. Evans, Mechanical Properties of the Red Cell Membrane in Relation to Molecular Structure and Genetic Defects, Annual Review of Biophysics and Biomolecular Structure, vol.23, issue.1, pp.787-803, 1994.
DOI : 10.1146/annurev.bb.23.060194.004035

G. Oradd, G. Wikander, G. Lindblom, and B. Johansson, H NMR, EPR and time-resolved fluorescence spectroscopy, J. Chem. Soc., Faraday Trans., vol.96, issue.2, pp.305-318, 1994.
DOI : 10.1039/FT9949000305

A. Palmer and J. Martin, Buckle propagation in submarine pipelines, Nature, vol.45, issue.5495, pp.46-61, 1975.
DOI : 10.1038/254046a0

G. Popescu, T. Ikeda, K. Goda, C. A. Best-popescu, M. L. Laposata et al., Optical Measurement of Cell Membrane Tension, Physical Review Letters, vol.97, issue.21, pp.218101-218113, 2006.
DOI : 10.1103/PhysRevLett.97.218101

P. Raux, P. Reis, J. Bush, and C. Clanet, Rolling Ribbons, Physical Review Letters, vol.105, issue.4, pp.44301-62, 2010.
DOI : 10.1103/PhysRevLett.105.044301
URL : https://hal.archives-ouvertes.fr/hal-01021116

E. Reyssat and L. Mahadevan, Hygromorphs: from pine cones to biomimetic bilayers, Journal of The Royal Society Interface, vol.17, issue.7024, p.951, 2009.
DOI : 10.1038/nature03185
URL : http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2838359

E. Reyssat and L. Mahadevan, How wet paper curls, EPL (Europhysics Letters), vol.93, issue.5, 2011.
DOI : 10.1209/0295-5075/93/54001

B. Salmon, A. Oksman, and D. Goldberg, Malaria parasite exit from the host erythrocyte: A two-step process requiring extraerythrocytic proteolysis, Proc. Natl. Acad
DOI : 10.1073/pnas.98.1.271

O. Sandre, L. Moreaux, and F. Brochard-wyart, Dynamics of transient pores in stretched vesicles, Proc. Natl. Acad. Sci. USA 96, pp.10591-10610, 1999.
DOI : 10.1073/pnas.96.19.10591

K. Seffen and S. Pellegrino, Deployment dynamics of tape springs, Proc. R. Soc. Lond. A 455, pp.1003-61, 1999.
DOI : 10.1098/rspa.1999.0347

U. Seifert, Configurations of fluid membranes and vesicles, Adv. Phys, p.14, 1997.

D. P. Siegel, Determining the Ratio of the Gaussian Curvature and Bending Elastic Moduli of Phospholipids from QII Phase Unit Cell Dimensions, Biophysical Journal, vol.91, issue.2, pp.608-618, 2006.
DOI : 10.1529/biophysj.106.085225

D. P. Siegel, The Gaussian Curvature Elastic Energy of Intermediates in Membrane Fusion, Biophysical Journal, vol.95, issue.11, pp.5200-5215, 2008.
DOI : 10.1529/biophysj.108.140152

D. P. Siegel and M. M. Kozlov, The Gaussian Curvature Elastic Modulus of N-Monomethylated Dioleoylphosphatidylethanolamine: Relevance to Membrane Fusion and Lipid Phase Behavior, Biophysical Journal, vol.87, issue.1, pp.366-382, 2004.
DOI : 10.1529/biophysj.104.040782

R. Songmuang, C. Deneke, and O. Schmidt, Rolled-up micro- and nanotubes from single-material thin films, Applied Physics Letters, vol.89, issue.22, pp.223109-223112, 2006.
DOI : 10.1063/1.2390647

S. Strogatz, Nonlinear dynamics and chaos: with applications to physics, biology, chemistry and engineering, Nonlinear dynamics and chaos, pp.34-1885, 2001.

D. Struik, Lectures on classical differential geometry, p.40, 1961.

L. Tadrist, F. Brochard-wyart, and D. Cuvelier, Bilayer curling and winding in a viscous fluid, Soft Matter, vol.19, issue.32, pp.8517-76, 2012.
DOI : 10.1039/c2sm25860a
URL : https://hal.archives-ouvertes.fr/hal-00996500

T. Umeda, Y. Suezaki, K. Takiguchi, and H. Hotani, Theoretical analysis of opening-up vesicles with single and two holes, Physical Review E, vol.71, issue.1, pp.11913-11942, 2005.
DOI : 10.1103/PhysRevE.71.011913

R. Verberg, I. Deschepper, and E. Cohen, Viscosity of colloidal suspensions, Physical Review E, vol.55, issue.3, pp.3143-3175, 1997.
DOI : 10.1103/PhysRevE.55.3143

R. Vermorel, N. Vandenberghe, and E. Villermaux, Radial Cracks in Perforated Thin Sheets, Physical Review Letters, vol.104, issue.17, pp.175502-71, 2010.
DOI : 10.1103/PhysRevLett.104.175502
URL : https://hal.archives-ouvertes.fr/hal-00566658

J. Veysey and N. Goldenfeld, Simple viscous flows: From boundary layers to the renormalization group, Reviews of Modern Physics, vol.79, issue.3, pp.45-68, 2007.
DOI : 10.1103/RevModPhys.79.883

G. Viamontes and D. Kirk, Cell shape changes and the mechanism of inversion in Volvox, The Journal of Cell Biology, vol.75, issue.3, p.719, 1977.
DOI : 10.1083/jcb.75.3.719

F. White, Fluid mechanics, p.45, 1979.

C. Williamson and R. Govardhan, VORTEX-INDUCED VIBRATIONS, Annual Review of Fluid Mechanics, vol.36, issue.1, pp.413-68, 2004.
DOI : 10.1146/annurev.fluid.36.050802.122128
URL : https://hal.archives-ouvertes.fr/hal-00091691

T. Witten and H. Li, Asymptotic Shape of a Fullerene Ball, Europhysics Letters (EPL), vol.23, issue.1, pp.51-51, 1993.
DOI : 10.1209/0295-5075/23/1/009

. Résumé, La déformation de matériaux élastiques dont l'une au moins des dimensions est petite apparaît dans un grand nombre de structures naturelles ou artificielles pour lesquelles une courbure spontanée est présente. Dans ces travaux de thèse, nous couplons plusieurs approches théoriques à des expériences macroscopiques sur des rubans élastiques afin de comprendre la dynamique d'enroulement de biomembranes ouvertes d'un trou. La motivation est issue d'observations récentes d'enroulements obtenues au cours de la sortie de parasites de la Malaria de globules rouges infectés (MIRBCs)

. Dans-une-première-partie, enroulement sur une biomembrane sphérique ouverte Nous modélisons de façon géométrique l'enroulement toroïdal de la membrane par une spirale d'Archimède de révolution et décentrée Avec cette hypothèse, nous montrons que la stabilité du pore vis-à-vis de l'enroulement dépend fortement de la tension de ligne et du cisaillement et nous discutons ces résultats dans le cadre de l'enroulement de membranes MIRBCs. De plus, en prenant en compte les différentes sources de dissipation, nous obtenons un très bon accord entre les données expérimentales obtenues pour les MIRBCs et la dynamique d'enroulement obtenue par le calcul. Notre approche montre en particulier que la dissipation dans la membrane due à la redistribution de la matière durant l'enroulement domine sur la dissipation visqueuse dans le milieu

L. Cependant, . Complexité-de-la-géométrie-sphérique, and . Ainsi-que-le-nombre-limité, échelle de la membrane sont une entrave au développement de modèles plus détaillés qui permettraient de décrire complètement le couplage entre écoulement et déformation Nous avons donc étudié dans une seconde partie la déformation d'enroulement dans le cas de rubans élastiques ayant une courbure spontanée dans différents milieux visqueux et pour différentes conditions élastiques. A grands nombres de Reynolds, en raison de la localisation de la courbure pour les rubans au cours de la propagation du front d'enroulement le long du matériau, nous montrons que l'enroulement atteint rapidement une vitesse de propagation constante. Dans ce régime, le ruban s'enroule sur lui-même de façon compacte, sur un cylindre dont la taille est prévue à partir d'une solution d'onde solitaire pour l'Elastica. A faible nombre de Reynolds, cependant, se rapprochant des conditions d'enroulement d'une membrane microscopique, nous mettons en évidence l'influence des forces de lubrification sur la nature non-compacte de l'enroulement, La taille globale de la spirale de ruban augmente dans le temps conduisant à une diminution de la puissance élastique libérée et donc à une diminution de la vitesse. Nous discutons dans quelle mesure ces résultats peuvent faire avancer la modélisation de l'enroulement dans les MIRBCs et les polymersomes