Anomalous transport of microswimmers in crowded environments

The common feature of biological and artificial self-propelled agents (active particles or microswimmers) is their ability to convert stored energy into directed motion at the micrometer scale. Examples include biological entities (bacteria or microorganisms) and artificial devices such as Janus particles or nanomotors. Here we will investigate the transport properties of such active agents in crowded environments consisting of obstacles, confining walls, ramified structures, and traps, in comparison to their passive counterparts undergoing merely Brownian motion as pioneered by Einstein. So far, transport and other properties of active particles were studied mainly in homogeneous environments, while only few experimental and theoretical works have been performed to explore the behavior of active agents in crowded environments. Yet, such studies are important from a practical point of view, as they are connected, for example, to the development of precise drug delivery and understanding of cancer metastasis. The problem therefore requires a thorough theoretical study extending the concepts developed for transport of passive particles which are known to display anomalous transport in such crowded environments. Our research aims at a complete and comprehensive explanation of the motion of complex microorganisms in realistic environments. Active particles differ from passive ones not only in the way they move, but, also how they interact with surfaces, walls, and obstacles. Two generic classes of microswimmers differing in the mechanism to generate flow have been identified: pullers and pushers. The first ones tend to run away from walls, while the second ones align to them. In particular, the angle of reflection in a scattering event is not equal to the angle of incidence, quite contrary to passive particles. This is a crucial factor that is anticipated to lead to drastic, essential differences in the quantitative and qualitative characteristics of their transport properties, in particular the anomalous dynamics will be strongly affected. In computer simulations the new scattering rules can be implemented efficiently and their ramifications on the transport properties be investigated in detail. Analytical calculations and simplified models will be used to rationalize the simulation results and thus provide a complete picture of the interplay of active motion and crowded environments.

The ability of motile microorganisms, such as bacteria, to navigate complex environments to solve their biological tasks is fascinating. Deeper understanding of this process comes from theoretical investigations based on the methods on non-equilibrium statistical physics. A model called active Brownian particle is employed to gain scientific progress. Microorganisms are known to follow the walls and surfaces so a model was also developed and implemented to efficiently take this interaction into account. Main result of the research project is that active particles moving in circles and with an ability to follow walls can spread fast through crowded environments and profit from large obstacle densities. This is shown in computer-based numerical simulations. In the theoretical limit of an ideal swimmer, existence of a slower than diffusion transport process - sub-diffusion - is shown. At low obstacle density ideal particle move following circular orbits hopping from one isolated obstacle cluster to another. If there are too few obstacles particle remains localized in some limited space. However, at a critical obstacle density when orbit radius becomes large enough to reach from any obstacle to its neighbors the sub-diffusion emerges. More realistic case of a swimmer subject to a random noise in its direction of motion exhibits both amplification and hinderance of diffusion. This is rationalized by the degree of imperfection of the trajectory and the characteristic distance of free travel inside the obstacle structure. Active swimming of circling particles under an influence of gravity was also considered. It has been revealed that spatial diffusivity exhibits a resonance behavior when external driving matches the internal rotational frequency. The investigation was inspired by an experiment on L-shaped artificial microswimmers driven by an influence of a laser light. In the experiment they were moving on an inclined surface and showed different trajectories depending on the inclination angle. We developed further a theory proposed in this work. Analytical calculations have shown that a complex interplay of three components self-rotation with self-propulsion, external torque, and angular noise leads to a resonance in trajectory diffusivity making it most randomized when external driving equals to internal and upon noise reaching zero. This is rationalized by mathematical properties of corresponding equations. Investigation of such properties was also an important part of the project and constitutes its important results. Other avenues of the project included active particle behavior in a landscape of varying diffusivity, which is important for experiments with active colloids. In such experiments the diffusivity can be controlled by the degree of illumination. Also, the hydrodynamic interactions of active particles with obstacles have been considered to make modelling more realistic.