@article{21384, abstract = {Cell migration in vivo is often guided by chemical signaling, i.e., chemotaxis. For immune cells performing chemotaxis in the organism, this process is influenced by the complex geometry of the tissue environment. In this study, we use a theoretical model of branched cell migration on a network to explore the cellular response to chemical gradients. The model predicts the response of a branched cell to a chemical gradient: how the cell reorients its internal polarity and how it navigates through a complex environment up a chemical gradient. We then compare the model’s predictions with experimental observations of neutrophils migrating to the site of a laser-inflicted wound in a zebrafish larva fin, and neutrophils migrating in vitro inside a regular lattice of pillars. We find that the model captures the details of the subcellular response to the chemokine gradient, as well as qualitative characteristics of the large-scale migration, suggesting that the neutrophils behave as fast cells, which explains the functionality of these immune cells.}, author = {Liu, Jiayi and Ron, Jonathan E. and Rinaldi, Giulia and Williantarra, Ivanna and Georgantzoglou, Antonios and de Vries, Ingrid and Sixt, Michael K and Sarris, Milka and Gov, Nir S.}, issn = {1553-7358}, journal = {PLOS Computational Biology}, number = {2}, publisher = {Public Library of Science}, title = {{Modelling chemotaxis of branched cells in complex environments provides insights into immune cell navigation}}, doi = {10.1371/journal.pcbi.1013934}, volume = {22}, year = {2026}, } @article{19702, abstract = {Moran Birth-death process is a standard stochastic process that is used to model natural selection in spatially structured populations. A newly occurring mutation that invades a population of residents can either fixate on the whole population or it can go extinct due to random drift. The duration of the process depends not only on the total population size n, but also on the spatial structure of the population. In this work, we consider the Moran process with a single type of individuals who invade and colonize an otherwise empty environment. Mathematically, this corresponds to the setting where the residents have zero reproduction rate, thus they never reproduce. The spatial structure is represented by a graph. We present two main contributions. First, in contrast to the Moran process in which residents do reproduce, we show that the colonization time is always at most a polynomial function of the population size n. Namely, we show that colonization always takes at most 1/2n^3 - 1/2n^2 expected steps, and for each n, we identify the slowest graph where it takes exactly that many steps. Moreover, we establish a stronger bound of roughly n^2.5 steps for undirected graphs and an even stronger bound of roughly n^2 steps for so-called regular graphs. Second, we discuss various complications that one faces when attempting to measure fixation times and colonization times in spatially structured populations, and we propose to measure the real duration of the process, rather than counting the steps of the classic Moran process.}, author = {Kopfová, Lenka and Tkadlec, Josef}, issn = {1553-7358}, journal = {PLoS computational biology}, number = {5}, pages = {e1012868}, publisher = {Public Library of Science}, title = {{Colonization times in Moran process on graphs}}, doi = {10.1371/journal.pcbi.1012868}, volume = {21}, year = {2025}, } @article{19640, abstract = {Synaptic plasticity is a key player in the brain’s life-long learning abilities. However, due to experimental limitations, the mechanistic link between synaptic plasticity rules and the network-level computations they enable remain opaque. Here we use evolutionary strategies (ES) to meta learn local co-active plasticity rules in large recurrent spiking networks with excitatory (E) and inhibitory (I) neurons, using parameterizations of increasing complexity. We discover rules that robustly stabilize network dynamics for all four synapse types acting in isolation (E-to-E, E-to-I, I-to-E and I-to-I). More complex functions such as familiarity detection can also be included in the search constraints. However, our meta learning strategy begins to fail for co-active rules of increasing complexity, as it is challenging to devise loss functions that effectively constrain network dynamics to plausible solutions a priori. Moreover, in line with previous work, we can find multiple degenerate solutions with identical network behaviour. As a local optimization strategy, ES provides one solution at a time and makes exploration of this degeneracy cumbersome. Regardless, we can glean the interdependecies of various plasticity parameters by considering the covariance matrix learned alongside the optimal rule with ES. Our work provides a proof of principle for the success of machine-learning-guided discovery of plasticity rules in large spiking networks, and points at the necessity of more elaborate search strategies going forward.}, author = {Confavreux, Basile J and Agnes, Everton J. and Zenke, Friedemann and Sprekeler, Henning and Vogels, Tim P}, issn = {1553-7358}, journal = {PLoS Computational Biology}, number = {4}, publisher = {Public Library of Science}, title = {{Balancing complexity, performance and plausibility to meta learn plasticity rules in recurrent spiking networks}}, doi = {10.1371/journal.pcbi.1012910}, volume = {21}, year = {2025}, } @article{15169, abstract = {Interpretation of extracellular recordings can be challenging due to the long range of electric field. This challenge can be mitigated by estimating the current source density (CSD). Here we introduce kCSD-python, an open Python package implementing Kernel Current Source Density (kCSD) method and related tools to facilitate CSD analysis of experimental data and the interpretation of results. We show how to counter the limitations imposed by noise and assumptions in the method itself. kCSD-python allows CSD estimation for an arbitrary distribution of electrodes in 1D, 2D, and 3D, assuming distributions of sources in tissue, a slice, or in a single cell, and includes a range of diagnostic aids. We demonstrate its features in a Jupyter Notebook tutorial which illustrates a typical analytical workflow and main functionalities useful in validating analysis results.}, author = {Chintaluri, Chaitanya and Bejtka, Marta and Sredniawa, Wladyslaw and Czerwinski, Michal and Dzik, Jakub M. and Jedrzejewska-Szmek, Joanna and Wojciki, Daniel K.}, issn = {1553-7358}, journal = {PLoS Computational Biology}, number = {3}, publisher = {Public Library of Science}, title = {{kCSD-python, reliable current source density estimation with quality control}}, doi = {10.1371/journal.pcbi.1011941}, volume = {20}, year = {2024}, } @article{15297, abstract = {Populations evolve by accumulating advantageous mutations. Every population has some spatial structure that can be modeled by an underlying network. The network then influences the probability that new advantageous mutations fixate. Amplifiers of selection are networks that increase the fixation probability of advantageous mutants, as compared to the unstructured fully-connected network. Whether or not a network is an amplifier depends on the choice of the random process that governs the evolutionary dynamics. Two popular choices are Moran process with Birth-death updating and Moran process with death-Birth updating. Interestingly, while some networks are amplifiers under Birth-death updating and other networks are amplifiers under death-Birth updating, so far no spatial structures have been found that function as an amplifier under both types of updating simultaneously. In this work, we identify networks that act as amplifiers of selection under both versions of the Moran process. The amplifiers are robust, modular, and increase fixation probability for any mutant fitness advantage in a range r ∈ (1, 1.2). To complement this positive result, we also prove that for certain quantities closely related to fixation probability, it is impossible to improve them simultaneously for both versions of the Moran process. Together, our results highlight how the two versions of the Moran process differ and what they have in common.}, author = {Svoboda, Jakub and Joshi, Soham Shrikant and Tkadlec, Josef and Chatterjee, Krishnendu}, issn = {1553-7358}, journal = {PLoS Computational Biology}, number = {3}, publisher = {Public Library of Science}, title = {{Amplifiers of selection for the Moran process with both Birth-death and death-Birth updating}}, doi = {10.1371/journal.pcbi.1012008}, volume = {20}, year = {2024}, } @article{18481, abstract = {A tight regulation of morphogen production is key for morphogen gradient formation and thereby for reproducible and organised organ development. Although many genetic interactions involved in the establishment of morphogen production domains are known, the biophysical mechanisms of morphogen source formation are poorly understood. Here we addressed this by focusing on the morphogen Sonic hedgehog (Shh) in the vertebrate neural tube. Shh is produced by the adjacently located notochord and by the floor plate of the neural tube. Using a data-constrained computational screen, we identified different possible mechanisms by which floor plate formation can occur, only one of which is consistent with experimental data. In this mechanism, the floor plate is established rapidly in response to Shh from the notochord and the dynamics of regulatory interactions within the neural tube. In this process, uniform activators and Shh-dependent repressors are key for establishing the floor plate size. Subsequently, the floor plate becomes insensitive to Shh and increases in size due to tissue growth, leading to scaling of the floor plate with neural tube size. In turn, this results in scaling of the Shh amplitude with tissue growth. Thus, this mechanism ensures a separation of time scales in floor plate formation, so that the floor plate domain becomes growth-dependent after an initial rapid establishment phase. Our study raises the possibility that the time scale separation between specification and growth might be a common strategy for scaling the morphogen gradient amplitude in growing organs. The model that we developed provides a new opportunity for quantitative studies of morphogen source formation in growing tissues.}, author = {Ho, Richard D.J.G. and Kishi, Kasumi and Majka, Maciej and Kicheva, Anna and Zagórski, Marcin P}, issn = {1553-7358}, journal = {PLoS Computational Biology}, publisher = {Public Library of Science}, title = {{Dynamics of morphogen source formation in a growing tissue}}, doi = {10.1371/journal.pcbi.1012508}, volume = {20}, year = {2024}, } @article{12862, abstract = {Despite the considerable progress of in vivo neural recording techniques, inferring the biophysical mechanisms underlying large scale coordination of brain activity from neural data remains challenging. One obstacle is the difficulty to link high dimensional functional connectivity measures to mechanistic models of network activity. We address this issue by investigating spike-field coupling (SFC) measurements, which quantify the synchronization between, on the one hand, the action potentials produced by neurons, and on the other hand mesoscopic “field” signals, reflecting subthreshold activities at possibly multiple recording sites. As the number of recording sites gets large, the amount of pairwise SFC measurements becomes overwhelmingly challenging to interpret. We develop Generalized Phase Locking Analysis (GPLA) as an interpretable dimensionality reduction of this multivariate SFC. GPLA describes the dominant coupling between field activity and neural ensembles across space and frequencies. We show that GPLA features are biophysically interpretable when used in conjunction with appropriate network models, such that we can identify the influence of underlying circuit properties on these features. We demonstrate the statistical benefits and interpretability of this approach in various computational models and Utah array recordings. The results suggest that GPLA, used jointly with biophysical modeling, can help uncover the contribution of recurrent microcircuits to the spatio-temporal dynamics observed in multi-channel experimental recordings.}, author = {Safavi, Shervin and Panagiotaropoulos, Theofanis I. and Kapoor, Vishal and Ramirez Villegas, Juan F and Logothetis, Nikos K. and Besserve, Michel}, issn = {1553-7358}, journal = {PLoS Computational Biology}, number = {4}, publisher = {Public Library of Science}, title = {{Uncovering the organization of neural circuits with Generalized Phase Locking Analysis}}, doi = {10.1371/journal.pcbi.1010983}, volume = {19}, year = {2023}, } @article{13230, abstract = {To interpret the sensory environment, the brain combines ambiguous sensory measurements with knowledge that reflects context-specific prior experience. But environmental contexts can change abruptly and unpredictably, resulting in uncertainty about the current context. Here we address two questions: how should context-specific prior knowledge optimally guide the interpretation of sensory stimuli in changing environments, and do human decision-making strategies resemble this optimum? We probe these questions with a task in which subjects report the orientation of ambiguous visual stimuli that were drawn from three dynamically switching distributions, representing different environmental contexts. We derive predictions for an ideal Bayesian observer that leverages knowledge about the statistical structure of the task to maximize decision accuracy, including knowledge about the dynamics of the environment. We show that its decisions are biased by the dynamically changing task context. The magnitude of this decision bias depends on the observer’s continually evolving belief about the current context. The model therefore not only predicts that decision bias will grow as the context is indicated more reliably, but also as the stability of the environment increases, and as the number of trials since the last context switch grows. Analysis of human choice data validates all three predictions, suggesting that the brain leverages knowledge of the statistical structure of environmental change when interpreting ambiguous sensory signals.}, author = {Charlton, Julie A. and Mlynarski, Wiktor F and Bai, Yoon H. and Hermundstad, Ann M. and Goris, Robbe L.T.}, issn = {1553-7358}, journal = {PLoS Computational Biology}, number = {6}, publisher = {Public Library of Science}, title = {{Environmental dynamics shape perceptual decision bias}}, doi = {10.1371/journal.pcbi.1011104}, volume = {19}, year = {2023}, } @article{12084, abstract = {Neuronal networks encode information through patterns of activity that define the networks’ function. The neurons’ activity relies on specific connectivity structures, yet the link between structure and function is not fully understood. Here, we tackle this structure-function problem with a new conceptual approach. Instead of manipulating the connectivity directly, we focus on upper triangular matrices, which represent the network dynamics in a given orthonormal basis obtained by the Schur decomposition. This abstraction allows us to independently manipulate the eigenspectrum and feedforward structures of a connectivity matrix. Using this method, we describe a diverse repertoire of non-normal transient amplification, and to complement the analysis of the dynamical regimes, we quantify the geometry of output trajectories through the effective rank of both the eigenvector and the dynamics matrices. Counter-intuitively, we find that shrinking the eigenspectrum’s imaginary distribution leads to highly amplifying regimes in linear and long-lasting dynamics in nonlinear networks. We also find a trade-off between amplification and dimensionality of neuronal dynamics, i.e., trajectories in neuronal state-space. Networks that can amplify a large number of orthogonal initial conditions produce neuronal trajectories that lie in the same subspace of the neuronal state-space. Finally, we examine networks of excitatory and inhibitory neurons. We find that the strength of global inhibition is directly linked with the amplitude of amplification, such that weakening inhibitory weights also decreases amplification, and that the eigenspectrum’s imaginary distribution grows with an increase in the ratio between excitatory-to-inhibitory and excitatory-to-excitatory connectivity strengths. Consequently, the strength of global inhibition reveals itself as a strong signature for amplification and a potential control mechanism to switch dynamical regimes. Our results shed a light on how biological networks, i.e., networks constrained by Dale’s law, may be optimised for specific dynamical regimes.}, author = {Christodoulou, Georgia and Vogels, Tim P and Agnes, Everton J.}, issn = {1553-7358}, journal = {PLoS Computational Biology}, number = {8}, publisher = {Public Library of Science}, title = {{Regimes and mechanisms of transient amplification in abstract and biological neural networks}}, doi = {10.1371/journal.pcbi.1010365}, volume = {18}, year = {2022}, } @article{12280, abstract = {In repeated interactions, players can use strategies that respond to the outcome of previous rounds. Much of the existing literature on direct reciprocity assumes that all competing individuals use the same strategy space. Here, we study both learning and evolutionary dynamics of players that differ in the strategy space they explore. We focus on the infinitely repeated donation game and compare three natural strategy spaces: memory-1 strategies, which consider the last moves of both players, reactive strategies, which respond to the last move of the co-player, and unconditional strategies. These three strategy spaces differ in the memory capacity that is needed. We compute the long term average payoff that is achieved in a pairwise learning process. We find that smaller strategy spaces can dominate larger ones. For weak selection, unconditional players dominate both reactive and memory-1 players. For intermediate selection, reactive players dominate memory-1 players. Only for strong selection and low cost-to-benefit ratio, memory-1 players dominate the others. We observe that the supergame between strategy spaces can be a social dilemma: maximum payoff is achieved if both players explore a larger strategy space, but smaller strategy spaces dominate.}, author = {Schmid, Laura and Hilbe, Christian and Chatterjee, Krishnendu and Nowak, Martin}, issn = {1553-7358}, journal = {PLOS Computational Biology}, keywords = {Computational Theory and Mathematics, Cellular and Molecular Neuroscience, Genetics, Molecular Biology, Ecology, Modeling and Simulation, Ecology, Evolution, Behavior and Systematics}, number = {6}, publisher = {Public Library of Science}, title = {{Direct reciprocity between individuals that use different strategy spaces}}, doi = {10.1371/journal.pcbi.1010149}, volume = {18}, year = {2022}, } @article{10939, abstract = {Understanding and characterising biochemical processes inside single cells requires experimental platforms that allow one to perturb and observe the dynamics of such processes as well as computational methods to build and parameterise models from the collected data. Recent progress with experimental platforms and optogenetics has made it possible to expose each cell in an experiment to an individualised input and automatically record cellular responses over days with fine time resolution. However, methods to infer parameters of stochastic kinetic models from single-cell longitudinal data have generally been developed under the assumption that experimental data is sparse and that responses of cells to at most a few different input perturbations can be observed. Here, we investigate and compare different approaches for calculating parameter likelihoods of single-cell longitudinal data based on approximations of the chemical master equation (CME) with a particular focus on coupling the linear noise approximation (LNA) or moment closure methods to a Kalman filter. We show that, as long as cells are measured sufficiently frequently, coupling the LNA to a Kalman filter allows one to accurately approximate likelihoods and to infer model parameters from data even in cases where the LNA provides poor approximations of the CME. Furthermore, the computational cost of filtering-based iterative likelihood evaluation scales advantageously in the number of measurement times and different input perturbations and is thus ideally suited for data obtained from modern experimental platforms. To demonstrate the practical usefulness of these results, we perform an experiment in which single cells, equipped with an optogenetic gene expression system, are exposed to various different light-input sequences and measured at several hundred time points and use parameter inference based on iterative likelihood evaluation to parameterise a stochastic model of the system.}, author = {Davidović, Anđela and Chait, Remy P and Batt, Gregory and Ruess, Jakob}, issn = {1553-7358}, journal = {PLoS Computational Biology}, number = {3}, publisher = {Public Library of Science}, title = {{Parameter inference for stochastic biochemical models from perturbation experiments parallelised at the single cell level}}, doi = {10.1371/journal.pcbi.1009950}, volume = {18}, year = {2022}, } @article{10535, abstract = {Realistic models of biological processes typically involve interacting components on multiple scales, driven by changing environment and inherent stochasticity. Such models are often analytically and numerically intractable. We revisit a dynamic maximum entropy method that combines a static maximum entropy with a quasi-stationary approximation. This allows us to reduce stochastic non-equilibrium dynamics expressed by the Fokker-Planck equation to a simpler low-dimensional deterministic dynamics, without the need to track microscopic details. Although the method has been previously applied to a few (rather complicated) applications in population genetics, our main goal here is to explain and to better understand how the method works. We demonstrate the usefulness of the method for two widely studied stochastic problems, highlighting its accuracy in capturing important macroscopic quantities even in rapidly changing non-stationary conditions. For the Ornstein-Uhlenbeck process, the method recovers the exact dynamics whilst for a stochastic island model with migration from other habitats, the approximation retains high macroscopic accuracy under a wide range of scenarios in a dynamic environment.}, author = {Bod'ová, Katarína and Szep, Eniko and Barton, Nicholas H}, issn = {1553-7358}, journal = {PLoS Computational Biology}, number = {12}, publisher = {Public Library of Science}, title = {{Dynamic maximum entropy provides accurate approximation of structured population dynamics}}, doi = {10.1371/journal.pcbi.1009661}, volume = {17}, year = {2021}, } @article{9381, abstract = {A game of rock-paper-scissors is an interesting example of an interaction where none of the pure strategies strictly dominates all others, leading to a cyclic pattern. In this work, we consider an unstable version of rock-paper-scissors dynamics and allow individuals to make behavioural mistakes during the strategy execution. We show that such an assumption can break a cyclic relationship leading to a stable equilibrium emerging with only one strategy surviving. We consider two cases: completely random mistakes when individuals have no bias towards any strategy and a general form of mistakes. Then, we determine conditions for a strategy to dominate all other strategies. However, given that individuals who adopt a dominating strategy are still prone to behavioural mistakes in the observed behaviour, we may still observe extinct strategies. That is, behavioural mistakes in strategy execution stabilise evolutionary dynamics leading to an evolutionary stable and, potentially, mixed co-existence equilibrium.}, author = {Kleshnina, Maria and Streipert, Sabrina S. and Filar, Jerzy A. and Chatterjee, Krishnendu}, issn = {1553-7358}, journal = {PLoS Computational Biology}, number = {4}, publisher = {Public Library of Science}, title = {{Mistakes can stabilise the dynamics of rock-paper-scissors games}}, doi = {10.1371/journal.pcbi.1008523}, volume = {17}, year = {2021}, } @article{9759, author = {Bartlett, Michael John and Arslan, Feyza N and Bankston, Adriana and Sarabipour, Sarvenaz}, issn = {1553-7358}, journal = {PLoS Computational Biology}, number = {7}, publisher = {Public Library of Science}, title = {{Ten simple rules to improve academic work- life balance}}, doi = {10.1371/journal.pcbi.1009124}, volume = {17}, year = {2021}, } @article{8767, abstract = {Resources are rarely distributed uniformly within a population. Heterogeneity in the concentration of a drug, the quality of breeding sites, or wealth can all affect evolutionary dynamics. In this study, we represent a collection of properties affecting the fitness at a given location using a color. A green node is rich in resources while a red node is poorer. More colors can represent a broader spectrum of resource qualities. For a population evolving according to the birth-death Moran model, the first question we address is which structures, identified by graph connectivity and graph coloring, are evolutionarily equivalent. We prove that all properly two-colored, undirected, regular graphs are evolutionarily equivalent (where “properly colored” means that no two neighbors have the same color). We then compare the effects of background heterogeneity on properly two-colored graphs to those with alternative schemes in which the colors are permuted. Finally, we discuss dynamic coloring as a model for spatiotemporal resource fluctuations, and we illustrate that random dynamic colorings often diminish the effects of background heterogeneity relative to a proper two-coloring.}, author = {Kaveh, Kamran and McAvoy, Alex and Chatterjee, Krishnendu and Nowak, Martin A.}, issn = {1553-7358}, journal = {PLOS Computational Biology}, keywords = {Ecology, Modelling and Simulation, Computational Theory and Mathematics, Genetics, Ecology, Evolution, Behavior and Systematics, Molecular Biology, Cellular and Molecular Neuroscience}, number = {11}, publisher = {Public Library of Science}, title = {{The Moran process on 2-chromatic graphs}}, doi = {10.1371/journal.pcbi.1008402}, volume = {16}, year = {2020}, } @article{7212, abstract = {The fixation probability of a single mutant invading a population of residents is among the most widely-studied quantities in evolutionary dynamics. Amplifiers of natural selection are population structures that increase the fixation probability of advantageous mutants, compared to well-mixed populations. Extensive studies have shown that many amplifiers exist for the Birth-death Moran process, some of them substantially increasing the fixation probability or even guaranteeing fixation in the limit of large population size. On the other hand, no amplifiers are known for the death-Birth Moran process, and computer-assisted exhaustive searches have failed to discover amplification. In this work we resolve this disparity, by showing that any amplification under death-Birth updating is necessarily bounded and transient. Our boundedness result states that even if a population structure does amplify selection, the resulting fixation probability is close to that of the well-mixed population. Our transience result states that for any population structure there exists a threshold r⋆ such that the population structure ceases to amplify selection if the mutant fitness advantage r is larger than r⋆. Finally, we also extend the above results to δ-death-Birth updating, which is a combination of Birth-death and death-Birth updating. On the positive side, we identify population structures that maintain amplification for a wide range of values r and δ. These results demonstrate that amplification of natural selection depends on the specific mechanisms of the evolutionary process.}, author = {Tkadlec, Josef and Pavlogiannis, Andreas and Chatterjee, Krishnendu and Nowak, Martin A.}, issn = {1553-7358}, journal = {PLoS computational biology}, publisher = {Public Library of Science}, title = {{Limits on amplifiers of natural selection under death-Birth updating}}, doi = {10.1371/journal.pcbi.1007494}, volume = {16}, year = {2020}, } @article{6784, abstract = {Mathematical models have been used successfully at diverse scales of biological organization, ranging from ecology and population dynamics to stochastic reaction events occurring between individual molecules in single cells. Generally, many biological processes unfold across multiple scales, with mutations being the best studied example of how stochasticity at the molecular scale can influence outcomes at the population scale. In many other contexts, however, an analogous link between micro- and macro-scale remains elusive, primarily due to the challenges involved in setting up and analyzing multi-scale models. Here, we employ such a model to investigate how stochasticity propagates from individual biochemical reaction events in the bacterial innate immune system to the ecology of bacteria and bacterial viruses. We show analytically how the dynamics of bacterial populations are shaped by the activities of immunity-conferring enzymes in single cells and how the ecological consequences imply optimal bacterial defense strategies against viruses. Our results suggest that bacterial populations in the presence of viruses can either optimize their initial growth rate or their population size, with the first strategy favoring simple immunity featuring a single restriction modification system and the second strategy favoring complex bacterial innate immunity featuring several simultaneously active restriction modification systems.}, author = {Ruess, Jakob and Pleska, Maros and Guet, Calin C and Tkačik, Gašper}, issn = {1553-7358}, journal = {PLoS Computational Biology}, number = {7}, publisher = {Public Library of Science}, title = {{Molecular noise of innate immunity shapes bacteria-phage ecologies}}, doi = {10.1371/journal.pcbi.1007168}, volume = {15}, year = {2019}, } @article{6900, 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.}, author = {Cepeda Humerez, Sarah A and Ruess, Jakob and Tkačik, Gašper}, issn = {1553-7358}, journal = {PLoS computational biology}, number = {9}, pages = {e1007290}, publisher = {Public Library of Science}, title = {{Estimating information in time-varying signals}}, doi = {10.1371/journal.pcbi.1007290}, volume = {15}, year = {2019}, }