Estimating information in time-varying signals

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.

The many bits of positional information

“…Several hypotheses exist to explain how cells can integrate PI from single morphogen gradients without thresholding or from multiple morphogen gradients. For example, cells could sense the difference or ratio of two opposing morphogen gradients (Houchmandzadeh et al, 2005;McHale et al, 2006), compare concentration values at two nearby spatial locations and thus estimate the local gradient (Mugler et al, 2016), or respond to temporal dynamics of the morphogen (Bergmann et al, 2007;Cepeda-Humerez et al, 2019). However, given the shapes and variabilities of gradients, the only statistically optimal possibility is the maximum a posteriori (MAP) decoding rule (Eqn 2).…”

Quantifying information accumulation encoded in the dynamics of biochemical signaling

“…However, such an analysis only provides a lower bound as it is unclear how much information might be lost in training the classifier. For example, classifiers employing linear principal components 29 may be inadequate to discriminate oscillatory and non-oscillatory trajectories.…”

IQCELL: A platform for predicting the effect of gene perturbations on developmental trajectories using single-cell RNA-seq data

“…In addition, new opportunities are arising to investigate the decision-making machinery of the cells in their native environment (via in-situ cell profiling) (Lee et al, 2015). The combination of these methods, prior knowledge of cellcell interactions (Browaeys et al, 2019;Kirouac et al, 2009), and emerging theoretical knowledge and computational technologies for capturing and quantifying spatio-temporal information content of cell signaling (Cepeda-Humerez et al, 2019;Dubuis et al, 2013;Maity & Wollman, 2020;Ostblom et al, 2019) can be used as invaluable resources for the next generation of GRN inference methods. These next-generation methods would ideally integrate cell signaling (P. Li & Elowitz, 2019) with GRNs directly from multi-omics sc data.…”