An asymptotic upscaling of transport across bacterial membranes

MollyBrennan

University College London

"An asymptotic upscaling of transport across bacterial membranes"

Multiscale problems are prevalent in many real world scenarios, especially in biology, where the behaviour of a single microorganism can have considerable impact over lengthscales much larger than its own. In this work we consider the effect of the membrane microstructure of a bacterial cell on the behaviour of concentration profiles of relevant molecules on bacterial and bacterial colony lengthscales. Transport through the outer membrane of gram-negative bacteria is restricted to specific channels and non-specific porins. These provide a size-restricted passageway for small molecules through an otherwise impermeable membrane. The effects of these channels are important, for example, antibiotics must cross the outer membrane in order to effectively target gram-negative bacteria, and quorum sensing molecules must cross the membrane to allow bacterial colonies to coordinate mass phenotypic changes such as the production of virulence factors. In mathematical models this limiting transport mechanism across the membrane is often represented via phenomenological constitutive boundary conditions. In this work, we systematically derive the correct effective boundary conditions to impose across a bacterial membrane in terms of physical channel and porin properties. We use a hybrid mathematical approach, combining multiscale methodology such as asymptotic homogenisation and boundary layer theory with numerical simulations. More broadly, because we consider a generic membrane geometry and do not impose a specific outer problem, the results that we derive have a wide scope of potential applications beyond bacterial membranes, for example, to model water vapour or heat loss through fabrics, or mass transfer through surface coatings in chemical engineering.
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