Although cells respond specifically to environments, how environmental identity is encoded intracellularly is not understood. Here, we study this organization of information in budding yeast by estimating the mutual information between environmental transitions and the dynamics of nuclear translocation for 10 transcription factors. Our method of estimation is general, scalable, and based on decoding from single cells. The dynamics of the transcription factors are necessary to encode the highest amounts of extracellular information, and we show that information is transduced through two channels: Generalists (Msn2/4, Tod6 and Dot6, Maf1, and Sfp1) can encode the nature of multiple stresses, but only if stress is high; specialists (Hog1, Yap1, and Mig1/2) encode one particular stress, but do so more quickly and for a wider range of magnitudes. In particular, Dot6 encodes almost as much information as Msn2, the master regulator of the environmental stress response. Each transcription factor reports differently, and it is only their collective behavior that distinguishes between multiple environmental states. Changes in the dynamics of the localization of transcription factors thus constitute a precise, distributed internal representation of extracellular change. We predict that such multidimensional representations are common in cellular decision-making.

Gene expression is controlled primarily by interactions between transcription factor proteins (TFs) and the regulatory DNA sequence, a process that can be captured well by thermodynamic models of regulation. These models, however, neglect regulatory crosstalk: the possibility that noncognate TFs could initiate transcription, with potentially disastrous effects for the cell. Here, we estimate the importance of crosstalk, suggest that its avoidance strongly constrains equilibrium models of TF binding, and propose an alternative nonequilibrium scheme that implements kinetic proofreading to suppress erroneous initiation. This proposal is consistent with the observed covalent modifications of the transcriptional apparatus and predicts increased noise in gene expression as a trade-off for improved specificity. Using information theory, we quantify this trade-off to find when optimal proofreading architectures are favored over their equilibrium counterparts. Such architectures exhibit significant super-Poisson noise at low expression in steady state.

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.

Although cells respond specifically to environments, how environmental identity is encoded intracellularly is not understood. Here we study this organization of information in budding yeast by estimating the mutual information between environmental transitions and the dynamics of nuclear translocation for ten transcription factors. Our method of estimation is general, scalable, and based on decoding from single cells. The dynamics of the transcription factors are necessary to encode the highest amounts of extracellular information, and we show that information is transduced through two channels: generalists (Msn2/4, Tod6/Dot6, Maf1, and Sfp1) can encode the nature of multiple stresses but only if stress is high; specialists (Hog1, Yap1, and Mig1/2) encode one particular stress, but do so more quickly and for a wider range of magnitudes. Each transcription factor reports differently, and it is only their collective response that distinguishes between multiple environmental states. Changes in the dynamics of the localization of transcription factors thus constitute a precise, distributed internal representation of extracellular change, and we predict that such multi-dimensional representations are common in cellular decision-making. Significance StatementTo thrive in diverse environments, cells must represent extracellular change intracellularly despite stochastic biochemistry. Here we introduce a quantitative framework for investigating the organization of information within a cell. Combining single-cell measurements of intracellular dynamics with a new, scalable methodology for estimating mutual information between time-series and a discrete input, we demonstrate that extracellular information is encoded in the dynamics of the nuclear localization of transcription factors and that information is lost with alternative static statistics. Any one transcription factor is usually insufficient, but the collective dynamics of multiple transcription factors can represent complex extracellular change. We therefore show that a cell's internal representation of its environment can be both distributed across diverse proteins and dynamically encoded.