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## Section: New Results

### Estimating information in time-varying signals

Participant : Jakob Ruess.

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. In [1], we developed and evaluated 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 derived model-based information approximations and analytical upper bounds, against which we benchmarked 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 applied these estimators to previously published data on Erk and Ca${}^{2+}$ signaling in mammalian cells and to yeast stress-response, and found that substantial amount of information about environmental state can be encoded by non-trivial response statistics even in stationary signals. We argued 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.