  Across diverse biological systems -- ranging from neural networks to
intracellular signaling and genetic regulatory networks -- the information
about changes in the environment is frequently encoded in the full temporal
dynamics of the network nodes. A pressing data-analysis challenge has thus been
to efficiently estimate the amount of information that these dynamics convey
from experimental data. Here we develop and evaluate decoding-based estimation
methods to lower bound the mutual information about a finite set of inputs,
encoded in single-cell high-dimensional time series data. For biological
reaction networks governed by the chemical Master equation, we derive
model-based information approximations and analytical upper bounds, against
which we benchmark our proposed model-free decoding estimators. In contrast to
the frequently-used k-nearest-neighbor estimator, decoding-based estimators
robustly extract a large fraction of the available information from
high-dimensional trajectories with a realistic number of data samples. We apply
these estimators to previously published data on Erk and Ca signaling in
mammalian cells and to yeast stress-response, and find that substantial amount
of information about environmental state can be encoded by non-trivial response
statistics even in stationary signals. We argue that these single-cell,
decoding-based information estimates, rather than the commonly-used tests for
significant differences between selected population response statistics,
provide a proper and unbiased measure for the performance of biological
signaling networks.
