Title: Mechanisms for bacterial gliding motility on soft substrates,
Abstract: The motility mechanism of certain rod-shaped bacteria has long been a
mystery, since no external appendages are involved in their motion which is
known as gliding. However, the physical principles behind gliding motility
still remain poorly understood. Using myxobacteria as a canonical example of
such organisms, we identify here the physical principles behind gliding
motility, and develop a theoretical model that predicts a two-regime behavior
of the gliding speed as a function of the substrate stiffness. Our theory
describes the elastic, viscous, and capillary interactions between the
bacterial membrane carrying a traveling wave, the secreted slime acting as a
lubricating film, and the substrate which we model as a soft solid. Defining
the myxobacterial gliding as the horizontal motion on the substrate under zero
net force, we find the two-regime behavior is due to two different mechanisms
of motility thrust. On stiff substrates, the thrust arises from the bacterial
shape deformations creating a flow of slime that exerts a pressure along the
bacterial length. This pressure in conjunction with the bacterial shape
provides the necessary thrust for propulsion. However, we show that such a
mechanism cannot lead to gliding on very soft substrates. Instead, we show that
capillary effects lead to the formation of a ridge at the slime-substrate-air
interface, which creates a thrust in the form of a localized pressure gradient
at the tip of the bacteria. To test our theory, we perform experiments with
isolated cells on agar substrates of varying stiffness and find the measured
gliding speeds to be in good agreement with the predictions from our
elasto-capillary-hydrodynamic model. The physical mechanisms reported here
serve as an important step towards an accurate theory of friction and
substrate-mediated interaction between bacteria in a swarm of cells
proliferating in soft media.