Kinematics of the swimming of Spiroplasma.

Spiroplasma swimming is studied with a simple model based on resistive-force theory. Specifically, we consider a bacterium shaped in the form of a helix that propagates traveling-wave distortions which flip the handedness of the helical cell body. We treat cell length, pitch angle, kink velocity, and distance between kinks as parameters and calculate the swimming velocity that arises due to the distortions. We find that, for a fixed pitch angle, scaling collapses the swimming velocity (and the swimming efficiency) to a universal curve that depends only on the ratio of the distance between kinks to the cell length. Simultaneously optimizing the swimming efficiency with respect to interkink length and pitch angle, we find that the optimal pitch angle is 35.5 degrees and the optimal interkink length ratio is 0.338, values in good agreement with experimental observations.

[1]  J E Avron,et al.  Optimal swimming at low Reynolds numbers. , 2004, Physical review letters.

[2]  Mark J. Schnitzer,et al.  Kinesin hydrolyses one ATP per 8-nm step , 1997, Nature.

[3]  D. Bromley,et al.  Axial filament involvement in the motility of Leptospira interrogans , 1979, Journal of bacteriology.

[4]  S. Trachtenberg,et al.  Motility modes of Spiroplasma melliferum BC3: a helical, wall‐less bacterium driven by a linear motor , 2003, Molecular microbiology.

[5]  S. Prager,et al.  Variational Treatment of Hydrodynamic Interaction in Polymers , 1969 .

[6]  R. Netz,et al.  Model for self-propulsive helical filaments: kink-pair propagation. , 2007, Physical review letters.

[7]  L. E. Becker,et al.  On self-propulsion of micro-machines at low Reynolds number: Purcell's three-link swimmer , 2003, Journal of Fluid Mechanics.

[8]  Daniel Tam,et al.  Optimal stroke patterns for Purcell's three-link swimmer. , 2006, Physical review letters.

[9]  P. Ocampo,et al.  On the Origin of the Treponematoses: A Phylogenetic Approach , 2008, PLoS neglected tropical diseases.

[10]  J. Gray,et al.  The Propulsion of Sea-Urchin Spermatozoa , 1955 .

[11]  H. Berg.  Random Walks in Biology , 2018 .

[12]  Lisa Fauci,et al.  Rotational dynamics of a superhelix towed in a Stokes fluid , 2007, 0706.3533.

[13]  S. Gould.  Syphilis and the Shepherd of Atlantis: The most "poetic" statement about the dreaded plague is not an early physician's hexameter but the modern map of the pathogen's genome. , 2000 .

[14]  D. Fletcher,et al.  Spiroplasma Swim by a Processive Change in Body Helicity , 2005, Cell.

[15]  S. F. Goldstein,et al.  Motility of the spirochete Leptospira. , 1988, Cell motility and the cytoskeleton.

[16]  C. Wolgemuth,et al.  The shape and dynamics of the Leptospiraceae. , 2007, Biophysical journal.

[17]  G. Fracastoro,et al.  Syphilis, sive, Morbus Gallicus , 2009 .

[18]  G. Oster,et al.  The motility of mollicutes. , 2003, Biophysical journal.

[19]  H. Hotani.  Light microscope study of mixed helices in reconstituted Salmonella flagella. , 1976, Journal of molecular biology.