# Estimating information in time-varying signals

## TL;DR

This paper introduces decoding-based methods to accurately estimate the mutual information conveyed by high-dimensional, time-varying biological signals, improving analysis of cellular responses to environmental changes.

## Contribution

It develops and benchmarks model-free decoding estimators for information quantification in complex biological time series data, outperforming traditional methods.

## Key findings

- Decoding estimators robustly extract information from high-dimensional trajectories.
- Significant environmental information is encoded in cellular response dynamics.
- Single-cell data reveals non-trivial response statistics carry environmental information.

## Abstract

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.