  In our previous publication, a framework for information flow in interaction
networks based on random walks with damping was formulated with two fundamental
modes: emitting and absorbing. While many other network analysis methods based
on random walks or equivalent notions have been developed before and after our
earlier work, one can show that they can all be mapped to one of the two modes.
In addition to these two fundamental modes, a major strength of our earlier
formalism was its accommodation of context-specific directed information flow
that yielded plausible and meaningful biological interpretation of protein
functions and pathways. However, the directed flow from origins to destinations
was induced via a potential function that was heuristic. Here, with a
theoretically sound approach called the channel mode, we extend our earlier
work for directed information flow. This is achieved by constructing a
potential function facilitating a purely probabilistic interpretation of the
channel mode. For each network node, the channel mode combines the solutions of
emitting and absorbing modes in the same context, producing what we call a
channel tensor. The entries of the channel tensor at each node can be
interpreted as the amount of flow passing through that node from an origin to a
destination. Similarly to our earlier model, the channel mode encompasses
damping as a free parameter that controls the locality of information flow.
Through examples involving the yeast pheromone response pathway, we illustrate
the versatility and stability of our new framework.
