Proliferating Active Matter and Living Electronics in Conductive Geobacter Biofilms

Electroactive biofilms of Geobacter sulfurreducens are model systems for long range extracellular electron transfer, yet they are usually described at the level of device performance rather than as concrete examples of proliferating active matter. In this paper I take the statistical mechanics point of view seriously and treat conductive Geobacter biofilms as driven, fluctuating media whose electronic transport properties co-evolve with growth, metabolism and internal redox fields. Building on experimental work that links redox gradients, metabolic stratification and cytochrome-based nanowire networks to long range conduction, I introduce a coarse-grained description in terms of cell density, nanowire density, nematic order and redox potential, with explicitly non-equilibrium noise that is not constrained by fluctuation-dissipation relations. Using this framework, I construct a simple one-dimensional toy model for a biofilm slab on an electrode and show how current-dependent growth and nanowire production naturally generate a self-organized conductive layer near the anode and intermittent conductive channels in marginal regions. I then connect these ideas to recent experiments on living electronics, including light-patterned electroactive biofilms, Geobacter protein nanowire memristors and genetically programmed extracellular electron transfer.