A. Ahmadi, M. C. Marchetti, and T. B. , Hydrodynamics of isotropic and liquid crystalline active polymer solutions, Physical Review E, vol.74, issue.6, pp.61913-56, 2006.
DOI : 10.1103/PhysRevE.74.061913

B. Alberts, A. Johnson, J. Lewis, M. Ra, K. Roberts et al., Molecular biology of the cell, p.55, 2002.

J. Allard and A. Mogilner, Traveling waves in actin dynamics and cell motility, Current Opinion in Cell Biology, vol.25, issue.1, p.131, 2012.
DOI : 10.1016/j.ceb.2012.08.012

F. Alouges, A. Desimone, and L. Heltai, NUMERICAL STRATEGIES FOR STROKE OPTIMIZATION OF AXISYMMETRIC MICROSWIMMERS, Mathematical Models and Methods in Applied Sciences, vol.21, issue.02, pp.361387-361427, 2011.
DOI : 10.1142/S0218202511005088

F. Alouges, A. Desimone, and A. Lefebvre, Optimal strokes for axisymmetric microswimmers, The European Physical Journal E, vol.28, issue.3, pp.279284-279324, 2009.
DOI : 10.1140/epje/i2008-10406-4

W. Alt and M. Dembo, Cytoplasm dynamics and cell motion: two-phase flow models, Mathematical Biosciences, vol.156, issue.1-2, pp.207-228, 1999.
DOI : 10.1016/S0025-5564(98)10067-6

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.476.4600

W. Alt and R. T. Tranquillo, BASIC MORPHOGENETIC SYSTEM MODELING SHAPE CHANGES OF MIGRATING CELLS: HOW TO EXPLAIN FLUCTUATING LAMELLIPODIAL DYNAMICS, Journal of Biological Systems, vol.03, issue.04, pp.3905916-128, 1995.
DOI : 10.1142/S0218339095000800

J. Steven, S. B. Altschuler, Y. Angenent, L. F. Wang, and . Wu, On the spontaneous emergence of cell polarity, Nature, issue.7206, pp.454886889-56, 2008.

J. C. Arciero, Q. Mi, M. F. Branca, D. J. Hackam, and D. Swigon, Continuum Model of Collective Cell Migration in Wound Healing and Colony Expansion, Biophysical Journal, vol.100, issue.3
DOI : 10.1016/j.bpj.2010.11.083

E. Atilgan, S. Wirtz, and . Sun, Morphology of the lamellipodium and organization of actin laments at the leading edge of crawling cells, Biophysical Journal, vol.89, issue.5 7, p.35893602, 2005.

E. Atilgan, S. Wirtz, and . Sun, Mechanics and Dynamics of Actin-Driven Thin Membrane Protrusions, Biophysical Journal, vol.90, issue.1, p.6576, 2006.
DOI : 10.1529/biophysj.105.071480

S. Banerjee and M. C. Marchetti, Substrate rigidity deforms and polarizes active gels, EPL (Europhysics Letters), vol.96, issue.2, pp.28003-137, 2011.
DOI : 10.1209/0295-5075/96/28003

URL : http://arxiv.org/abs/1106.0929

E. L. Barnhart, G. M. Allen, F. Julicher, and J. A. Theriot, Bipedal Locomotion in Crawling Cells, Biophysical Journal, vol.98, issue.6, pp.933942-114, 2010.
DOI : 10.1016/j.bpj.2009.10.058

E. L. Barnhart, K. Kun-chun-lee, A. Keren, J. A. Mogilner, and . Theriot, An Adhesion-Dependent Switch between Mechanisms That Determine Motile Cell Shape, PLoS Biology, vol.15, issue.Pt 22, pp.1001059-56, 2011.
DOI : 10.1371/journal.pbio.1001059.s022

A. Carlsson, P. Bayly, and L. Taber, Damped and persistent oscillations in a simple model of cell crawling, Journal of The Royal Society Interface, vol.18, pp.1742-5662, 2011.

G. Bell, Models for specic adhesion of cells to cells

P. Bellmichael-bellairs, R. Curtis, A. Dunn, and G. , Cell behavior -A tribute to Abercrombie, American Scientist, vol.72, issue.1 2, pp.8889-8901, 1984.

H. Berestycki, Equations de reaction-diusion et dynamiques de populations biologiques, UPMC, vol.24, p.26, 2008.

D. Bernardin, Introduction a la rheologie des uides : approche macroscopique Ecole de printemps, G.D.R. Materiaux vitreux, 20033.

A. Bernheim-groswasser, J. Prost, and C. Sykes, Mechanism of Actin-Based Motility: A Dynamic State Diagram, Biophysical Journal, vol.89, issue.2, pp.14111419-14111435, 2005.
DOI : 10.1529/biophysj.104.055822

A. Bershadsky, B. Balaban, and . Geiger, Adhesiondependent cell mechanosensitivity, Annual Review of Cell and Developmental Biology, vol.19, issue.12, pp.677695-159, 2003.
DOI : 10.1146/annurev.cellbio.19.111301.153011

D. Boal, Mechanics of the Cell, p.137, 2002.

J. S. Bois, F. Jülicher, and S. W. Grill, Pattern Formation in Active Fluids, Physical Review Letters, vol.106, issue.2, pp.28103-70, 2011.
DOI : 10.1103/PhysRevLett.106.028103

D. Bottino, . Mogilner, . Roberts, G. Stewart, and . Oster, How nematode sperm crawl, Journal of Cell Science, vol.115, issue.122, pp.367384-160, 2002.

D. Bray, Cell Movements: From Molecules to Motility, Garland Science, p.55, 2000.

J. Brugués and J. Casademunt, Self-Organization and Cooperativity of Weakly Coupled Molecular Motors under Unequal Loading, Physical Review Letters, vol.102, issue.11
DOI : 10.1103/PhysRevLett.102.118104

D. T. Burnette, S. Manley, P. Sengupta, R. Sougrat, M. W. Davidson et al., A role for actin arcs in the leading-edge advance of migrating cells, Nature Cell Biology, vol.79, issue.4, pp.371382-131, 2011.
DOI : 10.1038/ncb1655

E. Caglioti, P. L. Lions, C. Marchioro, and M. Pulvirenti, A special class of stationary ows for twodimensional euler equations: A statistical mechanics description, Communications in Mathematical Physics, vol.143, p.75, 1992.

W. John and . Cahn, On spinodal decomposition, Acta Metallurgica, vol.9, issue.9, pp.795-801, 1961.

A. C. Callan-jones and F. Julicher, Hydrodynamics of active permeating gels, New Journal of Physics, vol.13, issue.9, pp.17-137
DOI : 10.1088/1367-2630/13/9/093027

URL : https://hal.archives-ouvertes.fr/hal-00624806

V. Calvez, R. J. 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.594-608, 2012.
DOI : 10.1137/11083486X

V. Calvez, N. Meunier, and R. Voituriez, A one-dimensional Keller???Segel equation with a drift issued from the boundary, Comptes Rendus Mathematique, vol.348, issue.11-12, pp.629-634, 2010.
DOI : 10.1016/j.crma.2010.04.009

URL : https://hal.archives-ouvertes.fr/hal-00424649

O. Campas, L. Mahadevan, and J. Joanny, Actin Network Growth under Load, Biophysical Journal, vol.102, issue.5, p.137, 2012.
DOI : 10.1016/j.bpj.2012.01.030

L. Cardamone, A. Laio, V. Torre, R. Shahapure, and A. Desimone, Cytoskeletal actin networks in motile cells are critically selforganized systems synchronized by mechanical interactions, Proceedings of the National Academy of Sciences of the USA, pp.1397813983-157, 2011.

A. E. Carlsson, Mechanisms of cell propulsion by active stresses, New Journal of Physics, vol.13, issue.7, p.118, 2011.
DOI : 10.1088/1367-2630/13/7/073009

E. Anders, D. Carlsson, and . Sept, Mathematical modeling of cell migration, Biophysical tools for biologists, pp.911-56, 2008.

. Anderse, A. Carlsson, and . Mogilner, Mathematical and physical modeling of actin dynamics in motile cells

J. Carr and R. L. Pego, Metastable patterns in solutions of ut = e2 uxx -f(u), Communications on Pure and Applied Mathematics, vol.42, issue.5, pp.523576-84, 1989.

B. Chen and H. Gao, Mechanical Principle of Enhancing Cell-Substrate Adhesion via Pre-Tension in the Cytoskeleton, Biophysical Journal, vol.98, issue.10, pp.982154-2162, 2010.
DOI : 10.1016/j.bpj.2010.02.007

B. Chen and H. Gao, Mechanical Principle of Enhancing Cell-Substrate Adhesion via Pre-Tension in the Cytoskeleton, Biophysical Journal, vol.98, issue.10, pp.2154-2162, 2010.
DOI : 10.1016/j.bpj.2010.02.007

C. C. Chen and C. S. Lin, On the symmetry of blowup solutions to a mean eld equation, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, pp.271296-75, 2001.

T. N. Daniel, Q. Chen, P. A. Wen, J. C. Janmey, A. G. Crocker et al., Rheology of Soft Materials, Annual Review of Condensed Matter Physics Annual Review of Condensed Matter Physics, vol.1, issue.1 3, p.301322, 2010.

P. G. Ciarlet, Introduction a l'analyse numerique matricielle et a l'optimisation, p.162, 1988.

K. Clark, M. Langeslag, C. G. Figdor, and F. N. Van-leeuwen, Myosin II and mechanotransduction: a balancing act, Trends in Cell Biology, vol.17, issue.4, pp.178-186, 2007.
DOI : 10.1016/j.tcb.2007.02.002

B. Cleuren and C. Van-den-broeck, Brownian motion with absolute negative mobility, Physical Review E, vol.67, issue.5, p.120, 2003.
DOI : 10.1103/PhysRevE.67.055101

G. Csucs, K. Quirin, and G. Danuser, Locomotion of sh epidermal keratocytes on spatially selective adhesion patterns, Cell Motility and the Cytoskeleton, vol.64, issue.55, pp.856867-57, 2007.

D. V. Vladimir-igorevich-arnold and . Anosov, Dynamical Systems: Bifurcation theory and catastrophe theory

A. T. Dawes, G. B. Ermentrout, E. N. Cytrynbaum, and L. Edelstein-keshet, Actin lament branching and protrusion velocity in a simple 1D model of a motile cell, Journal Of Theoretical Biology, vol.242, issue.164, pp.265279-168, 2006.

P. Dimilla, D. Barbee, and . Lauenburger, Mathematical-model for the eects of adhesion and mechanics on cell-migration speed, Biophysical Journal, vol.60, issue.137, pp.1537-1555, 1991.

K. Doubrovinski and K. Kruse, Self-Organization of Treadmilling Filaments, Physical Review Letters, vol.99, issue.22, pp.228104-228120, 2007.
DOI : 10.1103/PhysRevLett.99.228104

K. Doubrovinski and K. Kruse, Self-organization in systems of treadmilling laments, European Physical Journal E, vol.31, issue.16, pp.95104-56, 2010.

K. Doubrovinski and K. Kruse, Cell Motility Resulting from Spontaneous Polymerization Waves, Physical Review Letters, vol.107, issue.25, pp.258103-115, 2011.
DOI : 10.1103/PhysRevLett.107.258103

A. Doyle and J. Lee, Cyclic changes in keratocyte speed and traction stress arise from Ca2+-dependent regulation of cell adhesiveness, Journal of Cell Science, vol.118, issue.2, pp.369379-164, 2005.
DOI : 10.1242/jcs.01590

X. Du, K. Doubrovinski, and M. Ostereld, Self-organized cell motility from motor-lament interactions

T. Erdmann and U. S. Schwarz, Stability of Adhesion Clusters under Constant Force, Physical Review Letters, vol.92, issue.10, p.108102, 2004.
DOI : 10.1103/PhysRevLett.92.108102

T. Erdmann and U. Schwarz, Stochastic dynamics of adhesion clusters under shared constant force and with rebinding, The Journal of Chemical Physics, vol.121, issue.18, p.89979017, 2004.
DOI : 10.1063/1.1805496

D. A. Fletcher and J. A. Theriot, An introduction to cell motility for the physical scientist, Physical Biology, vol.1, issue.1, pp.1-16, 2004.
DOI : 10.1088/1478-3967/1/1/T01

H. Gao, J. Qian, and B. Chen, Probing mechanical principles of focal contacts in cell-matrix adhesion with a coupled stochastic-elastic modelling framework, Journal of The Royal Society Interface, vol.106, issue.52, pp.12171232-53, 2011.
DOI : 10.1073/pnas.0904565106

M. L. Gardel, B. Sabass, L. Ji, G. Danuser, U. S. Schwarz et al., Traction stress in focal adhesions correlates biphasically with actin retrograde ow speed, Journal of Cell Biology, vol.183, issue.18, pp.9991005-159, 2008.

M. L. Gardel, I. C. Schneider, Y. Aratyn-schaus, and C. M. Waterman, Mechanical Integration of Actin and Adhesion Dynamics in Cell Migration, Annual Review of Cell and Developmental Biology, vol.26, issue.1, pp.315333-159, 2010.
DOI : 10.1146/annurev.cellbio.011209.122036

U. George, A. Stéphanou, and A. Madzvamuse, Mathematical modelling and numerical simulations of actin dynamics in the eukaryotic cell, Journal of Mathematical Biology, vol.2, issue.2, pp.147-161
DOI : 10.1007/s00285-012-0521-1

URL : https://hal.archives-ouvertes.fr/hal-00847003

F. Gerbal, P. Chaikin, Y. Rabin, and J. Prost, An Elastic Analysis of Listeria monocytogenes Propulsion, Biophysical Journal, vol.79, issue.5, pp.2259-2275, 2000.
DOI : 10.1016/S0006-3495(00)76473-3

F. Gladiali, M. Grossi, H. Ohtsuka, and T. Suzuki, Morse indices of multiple blow-up solutions to the two-dimensional gel'fand problem. arXiv preprint arXiv, pp.1210-1373, 2012.

E. Maria, H. G. Gracheva, and . Othmer, A continuum model of motility in ameboid cells, Bulletin of Mathematical Biology, vol.66, issue.1, pp.167-193, 2004.

W. Guo, N. Frey, Y. Burnham, and . Wang, Substrate Rigidity Regulates the Formation and Maintenance of Tissues, Biophysical Journal, vol.90, issue.6, pp.2213-2220, 2006.
DOI : 10.1529/biophysj.105.070144

P. Hanggi, F. Marchesoni, S. Savel-'ev, and G. Schmid, Asymmetry in shape causing absolute negative mobility, Physical Review E, vol.82, issue.4, p.120, 2010.
DOI : 10.1103/PhysRevE.82.041121

R. J. Hawkins, O. Bénichou, M. Piel, R. J. Voi-turiez-]-r, M. Hawkins et al., Rebuilding cytoskeleton roads: Activetransport-induced polarization of cells Pushing o the Walls: A Mechanism of Cell Motility in Connement, Physical Review E Physical Review Letters, vol.80, issue.14, pp.67-83, 2009.

R. J. Hawkins and R. Voituriez, Mechanisms of Cell Motion in Conned Geometries, Mathematical Modelling of Natural Phenomena, vol.5, issue.1, pp.84105-84119, 2010.

R. J. Hawkins, R. Poincloux, O. Benichou, M. Piel, P. Chavrier et al., Spontaneous Contractility-Mediated Cortical Flow Generates Cell Migration in Three-Dimensional Environments, Biophysical Journal, vol.101, issue.5
DOI : 10.1016/j.bpj.2011.07.038

M. Herant and M. Dembo, Form and Function in Cell Motility: From Fibroblasts to Keratocytes, Biophysical Journal, vol.98, issue.8, pp.14081417-115, 2010.
DOI : 10.1016/j.bpj.2009.12.4303

A. V. Hill, The Heat of Shortening and the Dynamic Constants of Muscle, Proceedings of the Royal Society of London. Series B, pp.136195-104, 1938.
DOI : 10.1098/rspb.1938.0050

D. Brenton, J. C. Homan, and . Crocker, Cell Mechanics: Dissecting the Physical Responses of Cells to Force, Annual Review of Biomedical Engineering, vol.11, pp.259288-113, 2009.

J. Howard, S. W. Grill, and J. S. Bois, Turing's next steps: the mechanochemical basis of morphogenesis, Nature Reviews Molecular Cell Biology, vol.26, issue.6, pp.392398-392412, 2011.
DOI : 10.1038/nrm3120

L. Hu and G. A. Papoian, Mechanochemical feedbacks regulate actin mesh growth in lamellipodial protrusions

H. Huxley, Electron microscope studies of the organisation of the laments in striated muscle, Biochimica et Biophysica Acta, vol.12, issue.3 8, p.387400, 1953.

H. Huxley, Muscle structure and theories of contraction, Progress in Biophysics and Molecular Biology, vol.7, issue.8, p.255, 1957.

A. Jilkine and L. Edelstein-keshet, A Comparison of Mathematical Models for Polarization of Single Eukaryotic Cells in Response to Guided Cues, PLoS Computational Biology, vol.89, issue.4, pp.1001121-65, 2011.
DOI : 10.1371/journal.pcbi.1001121.t003

J. F. Joanny, F. Julicher, K. Kruse, and J. Prost, Hydrodynamic theory for multi-component active polar gels, New Journal of Physics, vol.9, issue.11, p.137, 2007.
DOI : 10.1088/1367-2630/9/11/422

J. Joanny, J. Joanny, J. Julicher, and . Prost, Constructing Tools for the Description of Cell Dynamics Biological Physics: Poincare seminar Motion of an adhesive gel in a swelling gradient: A mechanism for cell locomotion, of Progress in Mathematical Physics 12th Poincare Seminar on Biological Physics, Inst Henri Poincare, pp.132-90, 2003.

K. John, P. Peyla, K. Kassner, J. Prost, and C. Misbah, Nonlinear Study of Symmetry Breaking in Actin Gels: Implications for Cellular Motility, Physical Review Letters, vol.100, issue.6, pp.14-114, 2008.
DOI : 10.1103/PhysRevLett.100.068101

D. D. Joseph, Fluid Dynamics of Viscoelastic Liquids, Applied Mathematical Sciences, vol.84, issue.3, 1990.
DOI : 10.1007/978-1-4612-4462-2

F. Julicher, J. Ajdari, and . Prost, Modeling molecular motors, Reviews of Modern Physics, vol.69, issue.4, pp.12691281-12691309, 1997.
DOI : 10.1103/RevModPhys.69.1269

F. Julicher, K. Kruse, J. Prost, and J. Joanny, Active behavior of the Cytoskeleton, Physics Reports, vol.449, issue.1-3, pp.328-124, 2007.
DOI : 10.1016/j.physrep.2007.02.018

K. Keren, Z. Pincus, G. M. Allen, E. L. Barnhart, G. Marriott et al., Mechanism of shape determination in motile cells, Nature, vol.15, issue.7194, pp.453475-453476, 2008.
DOI : 10.1038/nature06952

K. Keren, P. T. Yam, A. Kinkhabwala, A. Mogilner, and J. A. Theriot, Intracellular fluid flow in rapidly moving cells, Nature Cell Biology, vol.192, issue.10, pp.1219-137, 2009.
DOI : 10.1016/j.tcb.2003.09.002

J. Seob, K. , and S. X. Sun, Continuum modeling of forces in growing viscoelastic cytoskeletal networks, Journal of Theoretical Biology, vol.256, issue.4 7, p.596606, 2009.

S. Koehler, V. Schaller, and A. R. Bausch, Collective Dynamics of Active Cytoskeletal Networks, PLoS ONE, vol.179, issue.8, 2011.
DOI : 10.1371/journal.pone.0023798.s005

H. Gijsje, Z. Koenderink, F. Dogic, P. M. Nakamura, F. C. Bendix et al., An active biopolymer network controlled by molecular motors, Proceedings of the National Academy of Sciences of the USA, p.15192

T. Kole, Y. Tseng, . Jiang, D. Katz, and . Wirtz, Intracellular mechanics of migrating broblasts, Molecular Biology of the Cell, vol.16, issue.3, pp.328338-138, 2005.

K. Kruse, S. Camalet, and F. Julicher, Self-propagating patterns in active lament bundles, Physical Review Letters, vol.87, issue.128, p.131, 2001.

K. Kruse, J. F. Joanny, F. Julicher, and J. Prost, Contractility and retrograde ow in lamellipodium motion, Physical Biology, vol.3, issue.162, pp.130137-124, 2006.

K. Kruse, J. Joanny, . Julicher, K. Prost, and . Sekimoto, Generic theory of active polar gels: a paradigm for cytoskeletal dynamics, The European Physical Journal E, vol.9, issue.1, pp.516-533, 2005.
DOI : 10.1140/epje/e2005-00002-5

K. Kruse and F. Julicher, Actively Contracting Bundles of Polar Filaments, Physical Review Letters, vol.85, issue.8, pp.1778-1781, 2000.
DOI : 10.1103/PhysRevLett.85.1778

K. Kruse, A. Zumdieck, and F. Julicher, Continuum theory of contractile fibres, Europhysics Letters (EPL), vol.64, issue.5, pp.716-56, 2003.
DOI : 10.1209/epl/i2003-00618-2

K. Kruse and F. Julicher, Self-organization and mechanical properties of active lament bundles

K. Larripa and A. Mogilner, Transport of a 1D viscoelastic actin-myosin strip of gel as a model of a crawling cell. Physica A-Statistical Mechanics and its Applications, pp.113123-125, 2006.

E. Lauga and T. R. Powers, The hydrodynamics of swimming microorganisms, Reports on Progress in Physics, vol.72, issue.9, p.34, 2009.
DOI : 10.1088/0034-4885/72/9/096601

J. Lee, J. Ishihara, K. Theriot, and . Jacobson, Principles of locomotion for simple-shaped cells, Nature, vol.362, issue.6416, pp.167171-166, 1993.
DOI : 10.1038/362167a0

R. J. Leveque, Finite volume methods for hyperbolic problems, p.85, 2002.
DOI : 10.1017/CBO9780511791253

O. Lieleg, M. M. Claessens, and A. R. Bausch, Structure and dynamics of crosslinked actin networks, Soft Matter, vol.6, issue.2 2, p.218225, 2010.

O. Lieleg, K. M. Schmoller, C. J. Cyron, Y. Luan, W. A. Wall et al., Structural polymorphism in heterogeneous cytoskeletal networks, Soft Matter, vol.24, issue.2, p.17961803, 2009.
DOI : 10.1039/b814555p

M. L. Lombardi, D. A. Knecht, M. Dembo, and J. Lee, Traction force microscopy in Dictyostelium reveals distinct roles for myosin II motor and actin-crosslinking activity in polarized cell movement, Journal of Cell Science, vol.120, issue.9, pp.16241634-57, 2007.
DOI : 10.1242/jcs.002527

A. J. Loosley and J. X. Tang, Stick-slip motion and elastic coupling in crawling cells, Physical Review E, vol.86, issue.3, p.56
DOI : 10.1103/PhysRevE.86.031908

J. Lowengrub and L. Truskinovsky, Quasiincompressible cahn-hilliard uids and topological transitions, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, pp.45426172654-86, 1978.

L. Machura, M. Kostur, P. Talkner, J. Luczka, and P. Hanggi, Absolute negative mobility induced by thermal equilibrium uctuations, Physical Review Letters, vol.98, issue.4, p.120, 2007.

C. Frederick, C. F. Mackintosh, and . Schmidt, Active cellular materials, Current Opinion in Cell Biology, vol.22, issue.3, pp.2935-136, 2010.

Y. Marcy, . Prost, C. Carlier, and . Sykes, Forces generated during actin-based propulsion: A direct measurement by micromanipulation, Proceedings of the National Academy of Sciences of the USA, pp.59925997-59926012, 2004.
DOI : 10.1073/pnas.0307704101

M. Mayer, M. Depken, J. S. Bois, F. Julicher, and S. W. Grill, Anisotropies in cortical tension reveal the physical basis of polarizing cortical ows, Nature, issue.7315, pp.467617-150, 2010.

J. Mcgrath, C. Eungdamrong, . Fisher, . Peng, . Mahadevan et al., The forcevelocity relationship for the actin-based motility of Listeria monocytogenes, Current Biology, vol.13, issue.4, pp.329332-329348, 2003.

Q. Mi, D. Swigon, B. Riviere, S. Cetin, Y. Vodovotz et al., Onedimensional elastic continuum model of enterocyte layer migration, Biophysical Journal, issue.11, p.933745

S. Michelin and E. Lauga, Unsteady feeding and optimal strokes of model ciliates. arXiv preprint, p.40, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00996495

S. G. Mikhlin, Linear integral equations. Hindustan publishing corp, p.120, 1960.

T. Mitchison and L. Cramer, Actin-Based Cell Motility and Cell Locomotion, Cell, vol.84, issue.3, pp.371379-371392, 1996.
DOI : 10.1016/S0092-8674(00)81281-7

R. K. Mohammad and . Mofrad, Rheology of the Cytoskeleton, Annual Review of Fluid Mechanics, vol.41, issue.137, pp.433453-138, 2003.

A. Mogilner, On the edge: modeling protrusion, Current Opinion in Cell Biology, vol.18, issue.1, p.3239, 2006.
DOI : 10.1016/j.ceb.2005.11.001

A. Mogilner and L. Edelstein-keshet, Regulation of actin dynamics in rapidly moving cells: A quantitative analysis, Biophysical Journal, vol.83, issue.164, pp.12371258-168, 2002.

A. Mogilner and G. Oster, Cell motility driven by actin polymerization, Biophysical Journal, vol.71, issue.6, pp.3030-3045, 1996.
DOI : 10.1016/S0006-3495(96)79496-1

A. Mogilner, Mathematics of cell motility: have we got its number?, Journal of Mathematical Biology, vol.54, issue.101, pp.105134-105151, 2009.
DOI : 10.1007/s00285-008-0182-2

A. Mogilner, J. Allard, and R. Wollman, Cell Polarity: Quantitative Modeling as a Tool in Cell Biology, Science, vol.336, issue.6078
DOI : 10.1126/science.1216380

A. Mogilner, N. Ofer, and K. Keren, An actin 'disassembly clock' determines shape and speed of lamellipodial fragments, p.157, 2011.

V. Noireaux, R. M. Golsteyn, E. Friederich, J. Prost, C. Antony et al., Growing an Actin Gel on Spherical Surfaces, Biophysical Journal, vol.78, issue.3, pp.1643-1654, 2000.
DOI : 10.1016/S0006-3495(00)76716-6

H. Ohtsuka, A concentration phenomenon around a shrinking hole for solutions of mean eld equations

J. Oliver, . King, . Mckinlay, . Pd-brown, . Grant et al., Thin-lm theories for two-phase reactive ow models of active cell motion, Mathematical Medicine and Biology, vol.22, issue.1, pp.5398-5416, 2005.

F. Oosawa and S. Asakura, Thermodynamics of the polymerization of protein / Fumio Oosawa and Sho Asakura, 1975.

J. G. Orlandi, C. Blanch-mercader, and J. Casademunt, Cooperativity of self-organized Brownian motors pulling on soft cargoes, Physical Review E, vol.82, issue.6
DOI : 10.1103/PhysRevE.82.061903

N. Osterman and A. Vilfan, Finding the ciliary beating pattern with optimal eciency, Proceedings of the National Academy of Sciences, pp.1572715732-1572715772, 2011.

P. Panorchan, J. S. Lee, T. P. Kole, Y. Tseng, and D. Wirtz, Microrheology and ROCK Signaling of Human Endothelial Cells Embedded in a 3D Matrix, Biophysical Journal, vol.91, issue.9, pp.34993507-138, 2006.
DOI : 10.1529/biophysj.106.084988

A. Pathak, V. S. Deshpande, R. M. Mcmeeking, and A. G. Evans, The simulation of stress bre and focal adhesion development in cells on patterned substrates, Journal of the Royal Society Interface, vol.5, issue.3, pp.507524-137, 2008.

X. Peng, J. Huang, C. Xiong, and J. Fang, Cell adhesion nucleation regulated by substrate stiffness: A Monte Carlo study, Journal of Biomechanics, vol.45, issue.1, pp.116-122, 2012.
DOI : 10.1016/j.jbiomech.2011.09.013

B. Perthame and A. Dalibard, Existence of solutions of the hyperbolic Seller-Segel model. ArXiv Mathematics e-prints, p.90, 2006.

B. Perthame, C. Schmeiser, M. Tang, and N. Vauchelet, Travelling plateaus for a hyperbolic Keller???Segel system with attraction and repulsion: existence and branching instabilities, Nonlinearity, vol.24, issue.4, pp.12531270-90, 2011.
DOI : 10.1088/0951-7715/24/4/012

B. Perthame, Growth, reaction, movement and diusion from biology, UMPC, vol.14, issue.20, p.56, 2008.

C. Peskin, G. Odell, and . Oster, Cellular motions and thermal uctuations -The brownian ratchet, Biophysical Journal, vol.65, issue.6, pp.316324-120, 1993.

R. Poincloux, O. Collin, F. Lizárraga, M. Romao, M. Debray et al., Contractility of the cell rear drives invasion of breast tumor cells in 3D Matrigel, Proceedings of the National Academy of Sciences, p.57
DOI : 10.1073/pnas.1010396108

M. Prass, K. Jacobson, A. Mogilner, and M. Radmacher, Direct measurement of the lamellipodial protrusive force in a migrating cell, The Journal of Cell Biology, vol.7, issue.6, pp.767772-120, 2006.
DOI : 10.1083/jcb.200207148

J. Prost, C. Barbetta, and J. Joanny, Dynamical Control of the Shape and Size of Stereocilia and Microvilli, Biophysical Journal, vol.93, issue.4, pp.1124-1133, 2007.
DOI : 10.1529/biophysj.106.098038

J. Prost, J. Joanny, P. Lenz, and C. Sykes, The physics of listeria propulsion, In Cell Motility, Biological and Medical Physics Biomedical Engineering, pp.130-144, 2008.

E. M. Purcell, Life at low Reynolds number, American Journal of Physics, vol.45, issue.34, pp.311-65, 1977.

S. Rafelski and J. Theriot, Crawling toward a unied model of cell motility: Spatial and temporal regulation of actin dynamics, Annual Review of Biochemistry, vol.73, pp.209239-209256, 2004.

J. Ranft, J. Prost, F. Julicher, and J. F. Joanny, Tissue dynamics with permeation, The European Physical Journal E, vol.8, issue.6, p.136
DOI : 10.1140/epje/i2012-12046-5

X. Ren and L. Truskinovsky, Finite Scale Microstructures in Nonlocal Elasticity, Journal of Elasticity, vol.59, issue.65, pp.319355-96, 2000.
DOI : 10.1007/978-94-010-0728-3_18

A. J. Ridley, M. A. Schwartz, K. Burridge, R. A. Firtel, M. H. Ginsberg et al., Cell Migration: Integrating Signals from Front to Back, Science, vol.302, issue.5651, pp.30217041709-113, 2003.
DOI : 10.1126/science.1092053

A. Ros, . Eichhorn, . Regtmeier, . Duong, D. Reimann et al., Brownian motion: Absolute negative particle mobility, Nature, vol.75, issue.7053, pp.436928-120, 2005.
DOI : 10.1103/PhysRevE.67.055101

B. Rubinstein, M. F. Fournier, K. Jacobson, A. B. Verkhovsky, and A. Mogilner, Actin-Myosin Viscoelastic Flow in the Keratocyte Lamellipod, Biophysical Journal, vol.97, issue.7, pp.18531863-136, 2009.
DOI : 10.1016/j.bpj.2009.07.020

D. Saintillan and M. J. Shelley, Emergence of coherent structures and large-scale ows in motile suspensions, Journal of the Royal Society Interface, vol.9, issue.55, pp.571585-119, 2012.

G. Salbreux, J. Joanny, P. Prost, G. Pullarkat, J. Salbreux et al., Shape oscillations of non-adhering broblast cells Hydrodynamics of cellular cortical ows and the formation of contractile rings, Physical Biology Phys. Rev. Lett, vol.4268, issue.103, pp.161-159, 2007.

C. H. Schreiber, M. Stewart, and T. Duke, Simulation of cell motility that reproduces the force-velocity relationship, Proceedings of the National Academy of Sciences of the USA, pp.91419146-127, 2010.
DOI : 10.1073/pnas.1002538107

S. Ulrich, M. L. Schwarz, and . Gardel, United we stand, integrating the actin cytoskeleton and cell matrix adhesions in cellular mechanotransduction, Journal of Cell Science, vol.12, issue.18, p.159, 2012.

R. Shahapure, F. Difato, A. Laio, G. Bisson, E. Ercolini et al., Force Generation in Lamellipodia Is a Probabilistic Process with Fast Growth and Retraction Events, Biophysical Journal, vol.98, issue.6, pp.98979988-131, 2010.
DOI : 10.1016/j.bpj.2009.11.041

D. Shao, W. Rappel, and H. Levine, Computational Model for Cell Morphodynamics, Physical Review Letters, vol.105, issue.10, pp.56-114, 2010.
DOI : 10.1103/PhysRevLett.105.108104

M. Sheetz, H. Sable, and . Dobereiner, CONTINUOUS MEMBRANE-CYTOSKELETON ADHESION REQUIRES CONTINUOUS ACCOMMODATION TO LIPID AND CYTOSKELETON DYNAMICS, Annual Review of Biophysics and Biomolecular Structure, vol.35, issue.1, pp.417434-136, 2006.
DOI : 10.1146/annurev.biophys.35.040405.102017

M. Sheinman, C. P. Broedersz, and F. C. Mackintosh, Actively stressed marginal networks. ArXiv e-prints, p.136, 2012.
DOI : 10.1103/physrevlett.109.238101

URL : http://arxiv.org/abs/1206.4152

D. I. Shreiber, V. H. Barocas, and R. T. Tranquillo, Temporal variations in cell migration and traction during broblast-mediated gel compaction, Biophysical Journal, vol.84, issue.6, pp.41024114-41024134, 2003.

M. Shutova, C. Yang, J. M. Vasiliev, and T. Svitkina, Functions of Nonmuscle Myosin II in Assembly of the Cellular Contractile System, PLoS ONE, vol.586, issue.7, pp.2012-2052
DOI : 10.1371/journal.pone.0040814.s008

R. Simha and S. Ramaswamy, Hydrodynamic uctuations and instabilities in ordered suspensions of selfpropelled particles, Physical Review Letters, vol.89, issue.56, pp.55-119, 2002.

T. Stossel, On the crawling of animal cells, Science, vol.260, issue.5111, pp.10861094-113, 1993.
DOI : 10.1126/science.8493552

A. Stéphanou, E. Mylona, M. Chaplain, and P. Tracqui, A computational model of cell migration coupling the growth of focal adhesions with oscillatory cell protrusions, Journal of Theoretical Biology, vol.253, issue.4, pp.701-716, 2008.
DOI : 10.1016/j.jtbi.2008.04.035

D. Suzuki and T. Munakata, Rectification efficiency of a Brownian motor, Physical Review E, vol.68, issue.2, pp.21906-103, 2003.
DOI : 10.1103/PhysRevE.68.021906

T. Svitkina, . Verkhovsky, G. Km-mcquade, and . Borisy, Analysis of the Actin???Myosin II System in Fish Epidermal Keratocytes: Mechanism of Cell Body Translocation, The Journal of Cell Biology, vol.110, issue.2, pp.397-415, 1997.
DOI : 10.1002/cm.970250402

K. Tawada and K. Sekimoto, Protein friction exerted by motor enzymes through a weak-binding interaction, Journal of Theoretical Biology, vol.150, issue.2, pp.193200-159, 1991.
DOI : 10.1016/S0022-5193(05)80331-5

J. Theriot and T. Mitchison, Actin microlament dynamics in locomoting cells, Nature, vol.352, issue.6331, pp.126131-124, 1991.

J. Theriot, . Tj-mitchison, D. Tilney, and . Portnoy, The rate of actin-based motility of intracellular listeriamonocytogenes equals the rate of actin polymerization

P. G. Torres, I. B. Bischofs, and U. S. Schwarz, Contractile network models for adherent cells, Physical Review E, vol.85, issue.4, pp.2012-2020

P. G. Torres, K. Doubrovinski, and K. Kruse, Filament turnover stabilizes contractile cytoskeletal structures, EPL, vol.91, issue.58, p.61, 2010.

A. Van-oudenaarden and J. Theriot, Cooperative symmetry breaking by actin lament polymerization in a model for cell motility, Biophysical Journal, vol.78, issue.1 2, pp.1421-1435, 2000.

B. Vanderlei, J. J. Feng, and L. Edelstein-keshet, A Computational Model of Cell Polarization and Motility Coupling Mechanics and Biochemistry, Multiscale Modeling & Simulation, vol.9, issue.4, pp.14201443-14201463, 2011.
DOI : 10.1137/100815335

A. Verkhovsky, G. Svitkina, and . Borisy, Selfpolarization and directional motility of cytoplasm, Current Biology, vol.9, issue.57, pp.1120-55, 1999.

M. Vicente-manzanares, A. Webb, and . Horwitz, Cell migration at a glance, Journal of Cell Science, vol.118, issue.21, p.113, 2005.
DOI : 10.1242/jcs.02662

M. Vicente-manzanares, X. Ma, R. S. Adelstein, and A. R. Horwitz, Non-muscle myosin II takes centre stage in cell adhesion and migration, Nature Reviews Molecular Cell Biology, vol.19, issue.11
DOI : 10.1038/nrm2786

H. Wang and G. Oster, The Stokes eciency for molecular motors and its applications, Europhysics Letters, vol.57, issue.28, pp.134140-103, 2002.

Q. Wang, X. Yang, D. Adalsteinsson, T. C. Elston, K. Jacobson et al., Computational and Modeling Strategies for Cell Motility, pp.257296-257313, 2012.
DOI : 10.1007/978-1-4614-2146-7_11

Y. Wang, Y. Botvinick, . Zhao, . Berns, . Usami et al., Visualizing the mechanical activation of Src, Nature, vol.9, issue.7036, pp.43410401045-40, 2005.
DOI : 10.1016/S0960-9822(01)00583-8

H. Wolfenson, Y. I. Henis, B. Geiger, and A. D. Bershadsky, The heel and toe of the cell's foot: A multifaceted approach for understanding the structure and dynamics of focal adhesions, Cell Motility and the Cytoskeleton, vol.36, issue.Part 2
DOI : 10.1002/cm.20410

C. W. Wolgemuth, J. Stajic, and A. Mogilner, Redundant Mechanisms for Stable Cell Locomotion Revealed by Minimal Models, Cell Motility and the Cytoskeleton Biophysical Journal, vol.66187, issue.115, pp.1017-1029, 2009.

C. Wolgemuth, Lamellipodial Contractions during Crawling and Spreading, Biophysical Journal, vol.89, issue.3, pp.16431649-115, 2005.
DOI : 10.1529/biophysj.105.066720

URL : http://doi.org/10.1529/biophysj.105.066720

F. Wottawah, . Schinkinger, . Lincoln, . Ananthakrishnan, . Romeyke et al., Optical Rheology of Biological Cells, Physical Review Letters, vol.94, issue.9, p.138, 2005.
DOI : 10.1103/PhysRevLett.94.098103

M. Zajac, B. Dacanay, W. A. Mohler, and C. W. Wolgemuth, Depolymerization-driven ow in nematode spermatozoa relates crawling speed to size and shape, Biophysical Journal, vol.94, issue.122, pp.38103823-160, 2008.

M. H. Zaman, R. D. Kamm, P. Matsudaira, and D. A. Lauenburger, Computational Model for Cell Migration in Three-Dimensional Matrices, Biophysical Journal, vol.89, issue.2, pp.13891397-13891417, 2005.
DOI : 10.1529/biophysj.105.060723

N. Zebda, O. Dubrovskyi, and K. G. Birukov, Focal Adhesion Kinase Regulation of Mechanotransduction and its Impact on Endothelial Cell Functions, Microvascular Research, vol.83, issue.1, pp.71-81, 2012.
DOI : 10.1016/j.mvr.2011.06.007

W. Zhang, J. Qian, H. Yao, W. Chen, and H. Gao, Effects of functionally graded materials on dynamics of molecular bond clusters, Science China Physics, Mechanics and Astronomy, vol.4, issue.6, pp.980-988, 2012.
DOI : 10.1007/s11433-012-4726-5

Y. Zhong, D. Kong, L. Dai, and B. Ji, Frequency-Dependent Focal Adhesion Instability and Cell Reorientation Under Cyclic Substrate Stretching, Cellular and Molecular Bioengineering, vol.28, issue.3, p.442456, 2011.
DOI : 10.1007/s12195-011-0187-6

F. Ziebert, S. Swaminathan, and I. S. Aranson, Model for self-polarization and motility of keratocyte fragments, Journal of The Royal Society Interface, vol.6, issue.8, pp.10841092-115, 2012.
DOI : 10.1038/nmat1934

J. Zimmermann, C. Brunner, M. Enculescu, M. Goegler, A. Ehrlicher et al., Actin Filament Elasticity and Retrograde Flow Shape the Force-Velocity Relation of Motile Cells, Biophysical Journal, vol.102, issue.2, pp.287295-120, 2012.
DOI : 10.1016/j.bpj.2011.12.023