Locomotion of a single-flagellated bacterium


Naturally, flagellated bacteria move through swimming that involves various strategies dictated by the number and position of the flagella on the cell body. Technically, the movement of these bacteria is supported by rotary motors connected to the flagellar filament extended from the cell body. In the published literature, it has been shown that the forward and reverse swimming is as a result of the spinning of the flagellar motor and transmitting the motor rotation motion to the filament through a short compliant hook.

A monotrichous bacterium, for example, is capable of swimming either forward or backward when the hook is under compression and tension respectively. Lately researchers have focused on measuring the dynamic stiffening of the hook during steady swimming. Unfortunately, it has not given a clear picture of the causes and influence of subsequent parameters such as buckling and torsion.

Presently, several analytical and numerical methods like the boundary element method have been developed to study the dynamics of single-flagellated microorganisms. However, most of these techniques do not take into account the mechanical properties of the filament and the hook thus limiting their reliability.

To this note, Dr. Yunyoung Park, Yongsam Kim at Chung-Ang University together with Professor Sookkyung Lim at the University of Cincinnati developed a unique model for a freely swimming monotrichous bacterium. In particular, they designed a flexible filament and hook to enable bending and twisting. In addition, the authors achieved the rotation of the filament by rotating the motor only either by clockwise or counterclockwise and then transmitting the helical waves along the flagellum. They also investigated the interaction of the cell body and the flagellum and their corresponding effects. Their research work is currently published in the journal, Journal of Fluid Mechanics.

Briefly, the research team compared the swimming speeds and power efficiency with the previously obtained results to validate their mathematical model. Next, the influence of the different physical parameters such as rotational frequency on the swimming speed and rotation rate of the cell body was examined. Eventually, the relationship between the buckling angle and changing direction was explored to determine the critical threshold of the motor rotational frequency and the hook’s bending modulus.

The authors recorded swimming speeds and power efficiency of the cell similar to those initially obtained using the resistive force and slender body theories. However, the small discrepancy was attributed to the different driving force which was applied only at the motor rather than rotating the whole flagellum. Furthermore, it was worth noting that the swimming speed and the counterrotation rate of the cell body highly depended on the aspect ratio of the cell body.

In summary, the research team successfully investigated the locomotion of a single-flagellated bacterium. The influence of the variation in physical and geometrical properties of the hook and cell body exhibited significant effects on the buckling angle and swimming directions. For instance, heavier cell bodies turned with lesser degrees while slender cell bodies turned with larger degrees. This guarantees more degree of freedom to bacteria with rod-shaped cell bodies as compared to those with spherical cell bodies.

(Left) Backward and forward swimming motions of a monotrichous bacterium without a hook. The motor first rotates CW till t=50 ms and then switches to CCW rotation. When the motor rotates CW (CCW), the cell body counterrotates and the bacterium swims backward (forward).

(Right) Run-reverse-flick movement of a bacterium with a flexible hook. The rotation of motor changes CW to CCW at t= 20 ms, and the hook is more flexible from t=20 ms till t=50 ms when there occurs a buckling instability of the hook and the flicking of the cell body.


Locomotion-single-flagellated-bacterium -Advances-in-Engineering
Snapshots at some chosen times (left), and the trajectory of the dynamical motion of V. alginolyticus (right) which follows the order of start–reverse–flick–end. The motor frequency changes from -450 Hz to 450 Hz at t=20 ms. The hook is more flexible from t=20 ms to t=50 ms than the other time intervals, which induces a buckling instability of the hook and then reorientation of the bacterium.

About the author

Yongsam Kim is a professor in Department of Mathematics at Chung-Ang University in South Korea. His research area is computational fluid mechanics and mathematical biology. He is recently working on the locomotion of microorganisms, computational foam dynamics, vesicle motion in various fluid conditions, and the particle sedimentation in a non-Newtonian fluid.

About the author

Yunyoung Park is a postdoctoral researcher in the Innovation Center for Industrial Mathematics at National Institute for Mathematical Sciences in Republic of Korea. Her research interests are numerical simulations of locomotion of microorganisms, data analysis using machine learning and deep learning, and industrial mathematics.

About the author

Sookkyung Lim is a professor in the Department of Mathematical Sciences at the University of Cincinnati. Her research expertise lies in mathematical modeling, computer simulations, development of numerical algorithms, and analysis of dynamical processes to obtain insight into biological and physical problems. Currently her research is dedicated to studies of swimming microorganisms, cancer cell motility in the brain, and circadian rhythms.


Park, Y., Kim, Y., & Lim, S. (2018). Locomotion of a single-flagellated bacterium. Journal of Fluid Mechanics, 859, 586-612.

Go To Journal of Fluid Mechanics

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