Curvature-dependent dynamics of a bacterium confined in a giant unilamellar vesicle

We investigate the positional behavior of a single bacterium confined within a vesicle by measuring the probability of locating the bacterium at a certain distance from the vesicle boundary. We observe that the distribution is biexponential in nature. Near the boundary, the distribution exhibits rapid exponential decay, transitioning to a slower exponential decay, and eventually becoming uniform further away from the boundary. The length scales associated with the decay are found to depend on the confinement radius. We interpret these observations using molecular simulations and analytical calculations based on the Fokker-Planck equation for an active Brownian particle model. Our findings reveal that the small length scale is strongly influenced by the translational diffusion coefficient, while the larger length scale is governed by rotational diffusivity and self-propulsion. These results are explained in terms of two dimensionless parameters that explicitly include the confinement radius. The scaling behavior predicted analytically for the observed length scales is confirmed through simulations.