  Biological systems are known to communicate by diffusing chemical signals in
the surrounding medium. However, most of the recent literature has neglected
the electron transfer mechanism occurring amongst living cells, and its role in
cell-cell communication. Each cell relies on a continuous flow of electrons
from its electron donor to its electron acceptor through the electron transport
chain to produce energy in the form of the molecule adenosine triphosphate, and
to sustain the cell's vital operations and functions. While the importance of
biological electron transfer is well-known for individual cells, the past
decade has also brought about remarkable discoveries of multi-cellular
microbial communities that transfer electrons between cells and across
centimeter length scales, e.g., biofilms and multi-cellular bacterial cables.
These experimental observations open up new frontiers in the design of
electron-based communications networks in microbial communities, which may
coexist with the more well-known communication strategies based on molecular
diffusion, while benefiting from a much shorter communication delay. This paper
develops a stochastic model that links the electron transfer mechanism to the
energetic state of the cell. The model is also extensible to larger
communities, by allowing for electron exchange between neighboring cells.
Moreover, the parameters of the stochastic model are fit to experimental data
available in the literature, and are shown to provide a good fit.
