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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 Ca2+ 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.
Highlights
For their survival, reproduction, and differentiation, cells depend on their ability to respond and adapt to continually changing environmental conditions
We examined the performance of the Gaussian decoder when the mean steady state number of molecules in Example 2 in T < 1000 period is increased from 10 to 20, 50, or 100 by scaling up the production rates, to see consistent increases in decoder performance
We found that the simple one-layer network cannot extract any information; the threelayer network and several different two-layer networks can reach, but not exceed, the performance of the architecture used in the main figure given only N = 1000 samples, confirming our conclusion that higher performance requires significant increases in training set size independent of the neural network architecture
Summary
Reproduction, and differentiation, cells depend on their ability to respond and adapt to continually changing environmental conditions. Environmental information must be sensed and often transduced to the nucleus, where an appropriate response is initiated, usually by selectively up- or down-regulating the expression levels of target genes This information flow is mediated by biochemical reaction networks, in which concentrations of various signaling molecules code for different environmental states or different response programs. This map between environmental input or response output and the internal chemical state is, highly stochastic, because typical networks operate with small absolute copy numbers of signaling molecules [1]; different environments can be encoded by the same signaling molecule, by differentially regulating the dynamics of its concentration [2]. Applications of analogous techniques to biochemical signaling only started recently and represent an active area of research at the interface of physics, biology, statistics, and engineering [7,8,9,10]
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