  Motivated by recent discoveries of microbial communities that transfer
electrons across centimeter-length scales, this paper studies the information
capacity of bacterial cables via electron transfer, which coexists with
molecular communications, under the assumption of full causal channel state
information (CSI). The bacterial cable is modeled as an electron queue that
transfers electrons from the encoder at the electron donor source, which
controls the desired input electron intensity, to the decoder at the electron
acceptor sink. Clogging due to local ATP saturation along the cable is modeled.
A discrete-time scheme is investigated, enabling the computation of an
achievable rate. The regime of asymptotically small time-slot duration is
analyzed, and 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. A dynamic programming formulation of the
capacity is proposed, and the optimal binary signaling is determined via policy
iteration. It is proved that the optimal signaling 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 cable
distribution. In contrast, the optimal scheme balances the tension between
achieving high instantaneous information rate, and inducing a favorable
steady-state distribution, such that those states characterized by high
information rates are visited more frequently, thus revealing the importance of
CSI. This work represents a first contribution towards the design of electron
signaling schemes in complex microbial structures, e.g., bacterial cables and
biofilms, where the tension between maximizing the transfer of information and
guaranteeing the well-being of the overall bacterial community arises.
