Flagellar number governs bacterial spreading and transport efficiency

Peritrichous bacteria synchronize and bundle their flagella to actively swim, while disruption of the bundle leads to a slow motility phase with a weak propulsion. It is still not known whether the number of flagella represents an evolutionary adaptation toward optimizing bacterial navigation. We study the swimming dynamics of differentially flagellated Bacillus subtilis strains in a quasi-two-dimensional system. We find that decreasing the number of flagella N _f reduces the average turning angle between two successive run phases and enhances the run time and the directional persistence of the run phase. As a result, having fewer flagella is beneficial for long-distance transport and fast spreading, while having a lot of flagella is advantageous for the processes that require a slower spreading, such as biofilm formation. We develop a two-state random walk model that incorporates spontaneous switchings between the states and yields exact analytical expressions for transport properties, in remarkable agreement with experiments. The results of numerical simulations based on our two-state model suggest that the efficiency of searching and exploring the environment is optimized at intermediate values of N _f. The optimal choice of N _f, for which the search time is minimized, decreases with increasing the size of the environment in which the bacteria swim.