  Cells sense environmental signals and transmit information intracellularly
through changes in the abundance of molecular components. Such molecular
abundances can be measured in single cells and exhibit significant
heterogeneity in clonal populations even in identical environments.
Experimentally observed joint probability distributions can then be used to
quantify the covariability and mutual information between molecular abundances
along signaling cascades. However, because stationary state abundances along
stochastic biochemical reaction cascades are not conditionally independent,
their mutual information is not constrained by the data processing inequality.
Here, we report the conditions under which the mutual information between
stationary state abundances increases along a cascade of biochemical reactions.
This non-monotonic behavior can be intuitively understood in terms of noise
propagation and time-averaging stochastic fluctuations that are short-lived
compared to an extrinsic signal. Our results re-emphasize that mutual
information measurements of stationary state distributions of cellular
components may be of limited utility for characterizing cellular signaling
processes because they do not measure information transfer.
