Abstract.
We theoretically study the conformations of a helical semi-flexible filament confined to a flat surface. This squeezed helix exhibits a variety of unexpected shapes resembling circles, waves or spirals depending on the material parameters. We explore the conformation space in detail and show that the shapes can be understood as the mutual elastic interaction of conformational quasi-particles. Our theoretical results are potentially useful to determine the material parameters of such helical filaments in an experimental setting.
Graphical abstract
Similar content being viewed by others
References
O. Kahraman, N. Stoop, M.M. Müller, New J. Phys. 14, 095021 (2012)
N. Stoop, J. Najafi, F.K. Wittel, M. Habibi, Phys. Rev. Lett. 106, 214102 (2011)
J. Guven, P. Vázquez-Montejo, Phys. Rev. E 85, 026603 (2012)
H.P. Hsu, P. Grassberger, J. Chem. Phys. 120, 2034 (2004)
T. Sanchez, I.M. Kulić, Z. Dogic, Phys. Rev. Lett. 104, 098103 (2010)
J. Guven, D.M. Valencia, P. Vázquez-Montejo, J. Phys. A: Math. Theor. 47, 355201 (2014)
G.H.M. van der Heijden, Proc. R. Soc. London A 457, 695 (2001)
G.H.M. van der Heijden, A.R. Champneys, J.M.T. Thompson, Int. J. Solids Struct. 39, 1863 (2002)
G.H.M. van der Heijden, M.A. Peletier, R. Planqué, Arch. Ration. Mech. Anal. 182, 471 (2006)
G.H.M. van der Heijden, A.R. Champneys, J.M.T. Thompson, J. Mech. Phys. Solids 47, 59 (1999)
J.H. Maddocks, Arch. Ration. Mech. Anal. 85, 311 (1984)
H. Mohrbach, A. Johner, I.M. Kulić, Phys. Rev. Lett. 105, 268102 (2010)
H. Mohrbach, A. Johner, I.M. Kulić, Eur. Biophys. J. 41, 217 (2012)
C. Lu, M. Reedy, H.P. Erickson, J. Bacteriol. 182, 164 (2000)
S.M. Ferguson, P. De Camilli, Nat. Rev. Mol. Cell Biol. 13, 75 (2012)
S. Asakura, G. Eguchi, T. Iino, J. Mol. Biol. 16, 302 (1966)
A. Volodin et al., Phys. Rev. Lett. 84, 3342 (2000)
S.M. Douglas, J.J. Chou, W.M. Shih, Proc. Natl. Acad. Sci. U.S.A. 104, 6644 (2007)
G.M. Nam, N.K. Lee, H. Mohrbach, A. Johner, I.M. Kulić, EPL 100, 28001 (2012)
M. Nizette, A. Goriely, J. Math. Phys. 40, 2830 (1999)
O. Kahraman, H. Mohrbach, M.M. Müller, I.M. Kulić, Soft Matter 10, 2836 (2014)
N. Chouaieb, A. Goriely, J.H. Maddocks, Proc. Natl. Acad. Sci. U.S.A. 103, 9398 (2006)
M. Abramowitz, I.A. Stegun, Handbook of Mathematical Functions, 9th edition (Dover, Mineola, NY, 1970)
R.S. Manning, SIAM Rev. 51, 193 (2009)
J.F. Currie, J.A. Krumhans, A.R. Bishof, S.E. Trullinger, Phys. Rev. B 22, 477 (1980)
P. Gosselin, H. Mohrbach, I.M. Kulić, F. Ziebert, Physica D 318-319, 105 (2016)
G. Domokos, P. Holmes, B. Royce, J. Nonlinear Sci. 7, 281 (1997)
R.S. Manning, G.B. Bulman, Proc. R. Soc. London A: Math. Phys. Eng. Sci. 461, 2423 (2005)
B. Nöding, S. Köster, Phys. Rev. Lett. 108, 088101 (2012)
J.H. Maddocks, Arch. Ration. Mech. Anal. 99, 301 (1987)
I.M. Kulić, H. Mohrbach, V. Lobaskin, R. Thaokar, H. Schiessel, Phys. Rev. E 72, 041905 (2005)
I.M. Kulić, H. Mohrbach, R. Thaokar, H. Schiessel, Phys. Rev. E 75, 011913 (2007)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Bouzar, L., Müller, M.M., Gosselin, P. et al. Squeezed helical elastica. Eur. Phys. J. E 39, 114 (2016). https://doi.org/10.1140/epje/i2016-16114-6
Received:
Accepted:
Published:
DOI: https://doi.org/10.1140/epje/i2016-16114-6