Impacts of multiflagellarity on stability and speed of bacterial locomotion*

Trajectories and conformations of uni- and multiflagellar bacteria are studied with a coarse-grained model of elastic flagella connected to a cell body. The elasticities of both the hook protein (connecting cell body and flagellum) and flagella are varied. Flexibility plays contrasting roles for uni- and multiflagellar swimmers. For a uniflagellar swimmer, hook and/or flagellar buckling occurs above a critical flexibility relative to the torque exerted by the flagellar motor.  Addition of a second flagellum greatly expands the parameter regime of stable locomotion, because flexible hooks that would lead to buckling instability in the uniflagellar case provide the flexibility required for flagellar bundling in the biflagellar case. Similar observations hold for tri- and quadriflagellar swimmers. Indeed the stability regimes for uni- and quadriflagellar swimming are virtually inverted -- to a first approximation what is stable in one case is unstable in the other.   Swimming speed is also examined: it increases very weakly with number of flagella and a simple theory is developed that explains this observation.