Collective effects in ciliar arrays

Collective effects in one-dimensional ciliar arrays are studied analytically and numerically. A new phase oscillator description for ciliar motion is introduced which depends only on a single parameter. It allows the systematic study of hydrodynamic interactions between cilia exhibiting arbitrary beating patterns. It is shown that if the hydrodynamic interactions do not alter the beating pattern of the cilia no synchronization of ciliar motion occurs. This is in particular the case in arrays with low ciliar densities. But hydrodynamic interactions can lead to formation of a collective (metachronal) wave which is stable for periodic boundary conditions. In finite arrays free boundaries destroy this collective motion. The dispersion relation for metachronal waves is found to be non-universal, i.e., to depend crucially on the microscopic details of the ciliar beating pattern.

[1]  S. Gueron,et al.  Cilia internal mechanism and metachronal coordination as the result of hydrodynamical coupling. , 1997, Proceedings of the National Academy of Sciences of the United States of America.

[2]  M. Holwill,et al.  Biophysical aspects and modelling of ciliary motility. , 1995, Cell motility and the cytoskeleton.

[3]  S. Gueron,et al.  A three–dimensional model for ciliary motion based on the internal 9 + 2 structure , 2001, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[4]  M. Brueckner,et al.  Two Populations of Node Monocilia Initiate Left-Right Asymmetry in the Mouse , 2003, Cell.

[5]  C. Tabin,et al.  Left–right development: Conserved function for embryonic nodal cilia , 2002, Nature.

[6]  F. Jülicher,et al.  Membranes with rotating motors: Microvortex assemblies , 2004, The European physical journal. E, Soft matter.

[7]  Frank Jülicher,et al.  Hydrodynamic flow patterns and synchronization of beating cilia. , 2005, Physical review letters.

[8]  T. M. Sonneborn,et al.  The role of cortical orientation in the control of the direction of ciliary beat in Paramecium , 1975, The Journal of cell biology.

[9]  M. Cosentino Lagomarsino,et al.  Metachronal waves for deterministic switching two-state oscillators with hydrodynamic interaction. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  Synchronization of rotating helices by hydrodynamic interactions , 2004, The European physical journal. E, Soft matter.

[11]  Nakaoka,et al.  RECONSTITUTION OF METACHRONAL WAVES IN CILIATED CORTICAL SHEETS OF PARAMECIUM - WAVE STABILITIES , 1994, The Journal of experimental biology.

[12]  S. Gueron,et al.  Computation of the internal forces in cilia: application to ciliary motion, the effects of viscosity, and cilia interactions. , 1998, Biophysical journal.

[13]  J. Blake.  Microbiological fluid mechanics: a tribute to Sir James Lighthill , 2001 .

[14]  S. Tamm.  Mechanical synchronization of ciliary beating within comb plates of ctenophores. , 1984, The Journal of experimental biology.

[15]  C. Tabin,et al.  A two-cilia model for vertebrate left-right axis specification. , 2003, Genes & development.

[16]  Frank Jülicher,et al.  Membranes with rotating motors. , 2003, Physical review letters.

[17]  Christopher E. Brennen,et al.  Fluid Mechanics of Propulsion by Cilia and Flagella , 1977 .

[18]  R. Spigler,et al.  The Kuramoto model: A simple paradigm for synchronization phenomena , 2005 .

[19]  S. Vogel.  Life in Moving Fluids: The Physical Biology of Flow , 1981 .

[20]  T. Jahn,et al.  Locomotion of Protozoa , 1972 .

[21]  Y. Saijoh,et al.  Determination of left–right patterning of the mouse embryo by artificial nodal flow , 2002, Nature.

[22]  Z. Priel,et al.  Role of calcium and calmodulin in ciliary stimulation induced by acetylcholine. , 2001, American journal of physiology. Cell physiology.

[23]  B. Bassetti,et al.  Rowers coupled hydrodynamically. Modeling possible mechanisms for the cooperation of cilia , 2002 .

[24]  Hiroshi Hamada,et al.  Establishment of vertebrate left–right asymmetry , 2002, Nature Reviews Genetics.

[25]  S Gueron,et al.  Ciliary motion modeling, and dynamic multicilia interactions. , 1992, Biophysical journal.

[26]  O. Piro,et al.  Fluid-dynamical basis of the embryonic development of left-right asymmetry in vertebrates. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[27]  S. Mochón,et al.  The discrete-cilia approach to propulsion of ciliated micro-organisms , 1976, Journal of Fluid Mechanics.

[28]  F. Jülicher,et al.  Generic aspects of axonemal beating , 2000 .