How the motility pattern of bacteria affects their dispersal and chemotaxis

Abstract

Most bacteria at certain stages of their life cycle are able to move actively; they can swim in a liquid or crawl on various surfaces. A typical path of the moving cell often resembles the trajectory of a random walk. However, bacteria are capable of modifying their apparently random motion in response to changing environmental conditions. As a result, bacteria can migrate towards the source of nutrients or away from harmful chemicals. Surprisingly, many bacterial species that were studied have several distinct motility patterns, which can be theoretically modeled by a unifying random walk approach. We use this approach to quantify the process of cell dispersal in a homogeneous environment and show how the bacterial drift velocity towards the source of attracting chemicals is affected by the motility pattern of the bacteria. Our results open up the possibility of accessing additional information about the intrinsic response of the cells using macroscopic observations of bacteria moving in inhomogeneous environments.

Figure 1. Sketch of the predominant motility patterns.

a) Run-and-tumble, b) Run-reverse, and c) Run-reverse-flick. During a “run” event, a cell moves with high persistence. Runs are interrupted by reorientation events like tumbling or reversal. The time steps indicate the sequence of these events. An average turning angle after tumbling in E. coli bacteria is (a), whereas it is an almost perfect reversal of for many marine bacteria, or cells with twitching motility due to cell appendages, called pili (b). V. alginolyticus (c) alternates reversals (at ) with randomizing flicks (at ) with an average turning angle of .

Figure 2. Setup of the model.

A cell with velocity moves at constant speed . The angle between the velocity vector and the axis defines the direction of cell motion.

Figure 3. Velocity correlation function.

The normalized velocity correlation function is plotted as a function of dimensionless time . The curves are shown for run-and-tumble of E. coli with persistence parameter (red), run-reverse with (green), and run-reverse-flick with alternating and (blue). The analytical expressions are given in Eqs. (12) and (21), respectively.

Figure 4. Mean squared displacement (MSD).

The curves of the normalized MSD versus dimensionless time correspond to E. coli's run-and-tumble with (red), run-reverse with (green), and run-reverse-flick with alternating and (blue). The analytical expressions are given in Eqs. (13) and (22), respectively. The crosses are obtained from numerical simulations and fully agree with the analytical results.

Figure 5. Comparison of the chemotactic drift speed versus persistence parameter between run-tumble-flick [Eq. (28)] and run-tumble [Eq. (27)].

All parameters are adjusted to E. coli in the gradient with , , , and .

Figure 6. Chemotactic drift speed as a function of for E. coli and V. alginolyticus.

The plot on the left shows ; on the right, the chemotactic drift is normalized by the swimming speed as and coincides with the chemotactic index.