Kinematics of the swimming of Spiroplasma

TL;DR

This study models Spiroplasma swimming using resistive-force theory, revealing how cell shape and kink dynamics influence velocity and efficiency, with optimal parameters aligning with experimental data.

Contribution

Introduces a simple resistive-force theory model for Spiroplasma swimming, identifying optimal parameters consistent with experiments.

Findings

Swimming velocity scales with a universal curve based on kink spacing.

Optimal pitch angle is 35.5 degrees, matching experimental observations.

Optimal inter-kink length ratio is 0.338, consistent with empirical data.

Abstract

\emph{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 inter-kink length and pitch angle, we find that the optimal pitch angle is 35.5$^\circ$ and the optimal inter-kink length ratio is 0.338, values in good agreement with experimental observations.