Numerical Simulation of the Twitching Motility of Bacterium Crawling on a Solid Surface

Abstract

The size of most bacteria is about several micrometers in diameter, and motion of the bacteria is greatly influenced by viscous drag of the surrounding media[1]. Since the inertial motion is strongly restricted in such an environment, these bacteria skillfully use their appendages in order to move freely and autonomously. A common bacterium, e.g. Escherichia coli or Bacillus subtilis, is known to swim in liquid medium or to swarm on semisolid surfaces by rotating its flagella. Other bacterial species crawl over solid surfaces by extending and retracting their multiple pili. This motility is called ”twitching”, of which mechanism has been experimentally investigated on Pseudomonas aeruginosa[2] and Thermus thermophilus[3]. Though the alternating extension and retraction of bacterial pili should control the twitching motility, its mechanical and dynamical properties accompanied by the motion of pili are not fully understood. Here, we present a model of bacterium due to the twitching motility on solid surfaces and investigate characteristics of the bacterial motion by computer simulation (Fig.1). Our model of bacterial motion is based on Stokes’ law. Therefore, the drag force of the bacterial body in the viscous fluid balances with self-propelled force caused by retracting movement of the pili. In our simulation, when the single pilus is released from a surface of the medium, the balance of these forces is suddenly lost and the bacterial body turns in a short time like oversteering. This rapid motion is called ”slingshot” and found first in experiments[4]. According to the experiments, the average velocity of ”slingshot” is examined as ∼ 1.0μm/s which is faster than the retracting speed of the pilus ∼ 0.5μm/s. Thus, we can suggest that in spite of very small Reynolds numbers, bacteria powerfully locomote against a viscous fluid by means of retracting and releasing thier multiple pili to the surfaces skillfully.