A geometric criterion for the optimal spreading of active polymers in porous media

Christina Kurzthaler,Suvendu Mandal,Howard A Stone,Hartmut Löwen,Tapomoy Bhattacharjee,Sujit S Datta

doi:10.1038/s41467-021-26942-0

Abstract

Efficient navigation through disordered, porous environments poses a major challenge for swimming microorganisms and future synthetic cargo-carriers. We perform Brownian dynamics simulations of active stiff polymers undergoing run-reverse dynamics, and so mimic bacterial swimming, in porous media. In accord with experiments of Escherichia coli, the polymer dynamics are characterized by trapping phases interrupted by directed hopping motion through the pores. 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. 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 criterion unifies results for porous media with disparate pore sizes and shapes and for run-and-tumble polymers. It thus provides a fundamental principle for optimal transport of active agents in densely-packed biological and environmental settings.

Highlights

Efficient navigation through disordered, porous environments poses a major challenge for swimming microorganisms and future synthetic cargo-carriers
We propose that equation (2) serves as geometric criterion for optimal transport of active agents in porous media, which occurs when the run length lrun is comparable to the maximal pore length Lc;max characteristic of the porous the environment
We extend the concept of an ‘entropic trap’ model introduced in the study of diffusing long polymers escaping small outlets[41] and recently for E. coli bacteria moving in a porous medium[4,5]

Summary

Introduction

Porous environments poses a major challenge for swimming microorganisms and future synthetic cargo-carriers. While locomotion by swimming represents the most prominent, inevitable transport feature of many microorganisms, sudden changes of their swimming direction are an essential tool for their efficient search for nutrients[6] or escape from harmful environments[7] 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]. Their experiments indicated that smooth swimming strains of E. coli get stuck in the porous structure of the semi-solid agar, to incessantly tumbling cells, while at an intermediate tumbling rate bacterial transport appeared more efficient

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Results

Conclusion