Transition from active motion to anomalous diffusion for Bacillus subtilis confined in hydrogel matrices

We investigate the motility of B. subtilis under different degrees of confinement induced by transparent porous hydrogels. The dynamical behavior of the bacteria at short times is linked to characteristic parameters describing the hydrogel porosity. Mean squared displacements (MSDs) reveal that the run-and-tumble dynamics of unconfined B. subtilis progressively turns into sub-diffusive motion with increasing confinement. Correspondingly, the median instantaneous velocity of bacteria decreases and becomes more narrowly distributed, while the reorientation rate increases and reaches a plateau value. Analyzing single-trajectories, we show that the average dynamical behavior is the result of complex displacements, in which active, diffusive and sub-diffusive segments coexist. For small and moderate confinements, the number of active segments reduces, while the diffusive and sub-diffusive segments increase. The alternation of sub-diffusion, diffusion and active motion along the same trajectory can be described as a hopping ad trapping motion, in which hopping events correspond to displacements with an instantaneous velocity exceeding the corresponding mean value along a trajectory. Different from previous observations, escape from local trapping occurs for B. subtilis through active runs but also diffusion. Interestingly, the contribution of diffusion is maximum at intermediate confinements. At sufficiently long times transport coefficients estimated from the experimental MSDs under different degrees of confinement can be reproduced using a recently proposed hopping and trapping model. Finally, we propose a quantitative relationship linking the median velocity of confined and unconfined bacteria through the characteristic confinement length of the hydrogel matrix. Our work provides new insights for the bacterial motility in complex media that mimic natural environments and are relevant to important problems like sterilization, water purification, biofilm formation, membrane permeation and bacteria separation.