Reversals and collisions optimize protein exchange in bacterial swarms

Swarming groups of bacteria coordinate their behavior by self-organizing as a population to move over surfaces in search of nutrients and optimal niches for colonization. Many open questions remain about the cues used by swarming bacteria to achieve this self-organization. While chemical cue signaling known as quorum sensing is well-described, swarming bacteria often act and coordinate on time scales that could not be achieved via these extracellular quorum sensing cues. Here, cell-cell contact-dependent protein exchange is explored as a mechanism of intercellular signaling for the bacterium Myxococcus xanthus. A detailed biologically calibrated computational model is used to study how M. xanthus optimizes the connection rate between cells and maximizes the spread of an extracellular protein within the population. The maximum rate of protein spreading is observed for cells that reverse direction optimally for swarming. Cells that reverse too slowly or too fast fail to spread extracellular protein efficiently. In particular, a specific range of cell reversal frequencies was observed to maximize the cell-cell connection rate and minimize the time of protein spreading. Furthermore, our findings suggest that predesigned motion reversal can be employed to enhance the collective behavior of biological synthetic active systems.

Figure 1

Dependence of the $R_c$ on reversal periods. Solid circles represent $R_c$ for populations in simulations with different reversal periods. $R_c$ for the population of nonreversing cells was measured to be of the order of 0.46 connections/min. The filling fraction in the simulations was set at 12.8% close to the average fraction observed in experiments at the swarm edge. Solid squares display the distribution of reversal periods within a population of bacteria in an experiment obtained by calculating the fraction of observed bacteria $N\left(t_r\right)$ that reverse with period $t_r$ (adopted from [13]).

Figure 2

(a), (c), (e), and (g) Dependence of the average number of cell-cell connections on reversal frequency, flexibility, adhesion, and filling fraction, respectively. (b), (d), (f), and (h) Change of the normalized Shannon entropy $\widetilde{\mathrm{\Delta }I}\left(t\right)$ characterizing the distribution of protein over time in bacterial populations with different reversal frequencies, cell flexibilities, cell-cell adhesions, and filling fraction, respectively. (See the Appendixes for details about measurement and normalization of entropy.)

Figure 3

(a), (c), (e), and (g) Dependence of the average connection duration on the reversal period, bending rigidity, adhesion strength, and number density, respectively. (b), (d), (f), and (h) Clustering behavior for different (low, calibrated with experiments, and high) values of reversal period, bending rigidity, adhesion strength, and number density, respectively.

Figure 4

Initial cell distributions in simulations of the populations with densities 6.4% (a), 12.8% (b), and 20% (c). The size of the simulation domain is set to $100\times 100$ $\mu {\text{m}}^2$ and the length of the cells is 5 $\mu \text{m}$. The color scale shows the level of the protein on each cell that is chosen randomly from a uniform distribution from [0, 1].

Figure 5

Normalized protein distribution at time $t$. Initial protein levels of cells are chosen from a uniform random distribution. Over time, cells make connections and exchange protein with each other. The level of protein on all cells approaches the same value $n_k=0.5$ assuming that enough time is given. Population consists of 512 cells moving inside a 2D simulation domain of the size $100\times 100$ $\mu {\text{m}}^2$.

Figure 6

Representation of cells with SCEs. White spheres and segments indicate positions and bonds of SCEs. The green (outer) shell represents the boundary for the zone of attraction, and the cyan (inner) shell represents the boundary of the repulsive force. (Repulsion and attraction zones are not to exact scale.) Red SCEs highlight stretching interactions between SCEs. Blue SCEs represent the bending interaction between SCEs.