Systems of rod-shaped viruses have long been important to the science of living liquid crystals, as their monodispersity and uniform charge make them convenient model systems. Recently, it was shown that, upon the addition of polymers, suspensions of rod-shaped viruses form liquid crystals that are linked with increased tolerance of bacteria against antibiotics. We use homogenization to obtain effective equations describing antibiotic diffusion through these liquid crystals. The analytical results of homogenization are compared with numerical results from an exact microscopic model, showing good agreement and thus allowing us to identify the key parameters behind the process. Our modelling shows that the adsorption plays a key role in increasing antibiotic diffusion time and therefore the presence of nematic rod-shaped viruses may increase antibiotic tolerance through physical mechanisms alone. These results demonstrate the applicability of homogenization as an analytical tool to systems of liquid crystalline viruses, with relatively straightforward extension to more complex problems such as liquid crystalline biofilms, other biological liquid crystals and biological systems with different types of local structural order.
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