Capacity of bacterial cables via Electron-transfer under full-CSI

Recent discoveries of bacterial cables that transfer electrons across centimeter-length scales motivate the study of their information capacity. The bacterial cable is modeled as an electron queue that transfers electrons from the encoder at the electron donor source to the decoder at the electron acceptor sink. The model allows to capture the coupling between the electron signal and the energetic state of the cells via clogging due to local ATP saturation along the cable. Based on the analysis of a discrete-time scheme with asymptotically small time-slot duration, and assuming full causal channel state information (CSI), the optimality of binary input distributions is proved, i.e., the encoder transmits at either maximum or minimum intensity, as dictated by the physical constraints of the cable. It is proved that the optimal binary signal can be determined via dynamic programming, and that it has smaller intensity than that given by the myopic policy, which greedily maximizes the instantaneous information rate but neglects its effect on the steady-state distribution of the cable. This work represents a first contribution towards the design of electron signaling schemes in more complex microbial systems, e.g., biofilms, where the tension between maximizing the transfer of information and guaranteeing the well-being of the overall bacterial community arises, and motivates further research on the design of more practical schemes, where CSI is only partially available.