In fact, randomizing the swimming direction of these autonomous agents could be an efficient strategy for reaching a target. Yet, their ability to self-propel might not suffice to make them generally suitable for performing complex tasks in biomedical and environmental settings, where, for example, they may be expected to deliver drugs to a specific target 19, penetrate the porous structure of tumors 20, 21, or find and induce degradation of contaminants 16, 22. Understanding the underlying physical mechanisms is thus paramount for revealing fundamental microbiological processes, such as biofilm formation and community ecology 13, 14, and has significant potential to enable novel nanotechnological applications 15, 16.Įngineering the propulsive mechanisms of microorganisms has proven to be a promising route towards the design and development of smart, self-propelled cargo-carriers 17, 18 that overcome several limitations of their passive counterparts (e.g., ordinary colloids). In unconfined media these transport features lead to trajectories reminiscent of a random walk, yet their consequences for the navigation through real, porous environments, characteristic of a wide variety of biological, biomedical, and environmental contexts, such as biological gels and tissues or environmental soils and sediments, remain largely unexplored. These reorientation events are generated by intrinsic biophysical mechanisms and generate different swimming modes, such as the run-and-tumble motion of Escherichia coli 3 or Bacillus subtilis 8, run-reverse(-flick) patterns of diverse bacteria 9, 10, sharp turns in swimming algae 11, and run-reverse behavior of different species of archaea 12. While locomotion by swimming represents the most prominent, inevitable transport feature of many microorganisms, sudden changes of their swimming direction are also an essential tool for their efficient search for nutrients 6 or escape from harmful environments 7. Microorganisms display agile motility features to optimize their survival strategies and efficiently navigate through their natural disordered and porous habitats 1, 2, 3, 4, 5. It thus provides a fundamental principle for optimal transport of active agents in densely-packed biological and environmental settings.
Our criterion unifies results for porous media with disparate pore sizes and shapes and for run-and-tumble polymers.
More significantly, we discover a geometric criterion for the optimal spreading, which emerges when their run lengths are comparable to the longest straight path available in the porous medium. Our findings show that the spreading of active agents in porous media can be optimized by tuning their run lengths, which we rationalize using a coarse-grained model. In accord with experiments of Escherichia coli, the polymer dynamics are characterized by trapping phases interrupted by directed hopping motion through the pores. We perform Brownian dynamics simulations of active stiff polymers undergoing run-reverse dynamics, and so mimic bacterial swimming, in porous media. Efficient navigation through disordered, porous environments poses a major challenge for swimming microorganisms and future synthetic cargo-carriers.