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1.
Cell ; 185(2): 345-360.e28, 2022 01 20.
Article in English | MEDLINE | ID: mdl-35063075

ABSTRACT

We present a whole-cell fully dynamical kinetic model (WCM) of JCVI-syn3A, a minimal cell with a reduced genome of 493 genes that has retained few regulatory proteins or small RNAs. Cryo-electron tomograms provide the cell geometry and ribosome distributions. Time-dependent behaviors of concentrations and reaction fluxes from stochastic-deterministic simulations over a cell cycle reveal how the cell balances demands of its metabolism, genetic information processes, and growth, and offer insight into the principles of life for this minimal cell. The energy economy of each process including active transport of amino acids, nucleosides, and ions is analyzed. WCM reveals how emergent imbalances lead to slowdowns in the rates of transcription and translation. Integration of experimental data is critical in building a kinetic model from which emerges a genome-wide distribution of mRNA half-lives, multiple DNA replication events that can be compared to qPCR results, and the experimentally observed doubling behavior.


Subject(s)
Cells/cytology , Computer Simulation , Adenosine Triphosphate/metabolism , Cell Cycle/genetics , Cell Proliferation/genetics , Cells/metabolism , DNA Replication/genetics , Gene Expression Regulation , Imaging, Three-Dimensional , Kinetics , Lipids/chemistry , Metabolic Networks and Pathways , Metabolome , Molecular Sequence Annotation , Nucleotides/metabolism , Thermodynamics , Time Factors
2.
Cell ; 184(10): 2767-2778.e15, 2021 05 13.
Article in English | MEDLINE | ID: mdl-33857423

ABSTRACT

Individual neurons in visual cortex provide the brain with unreliable estimates of visual features. It is not known whether the single-neuron variability is correlated across large neural populations, thus impairing the global encoding of stimuli. We recorded simultaneously from up to 50,000 neurons in mouse primary visual cortex (V1) and in higher order visual areas and measured stimulus discrimination thresholds of 0.35° and 0.37°, respectively, in an orientation decoding task. These neural thresholds were almost 100 times smaller than the behavioral discrimination thresholds reported in mice. This discrepancy could not be explained by stimulus properties or arousal states. Furthermore, behavioral variability during a sensory discrimination task could not be explained by neural variability in V1. Instead, behavior-related neural activity arose dynamically across a network of non-sensory brain areas. These results imply that perceptual discrimination in mice is limited by downstream decoders, not by neural noise in sensory representations.


Subject(s)
Discrimination, Psychological/physiology , Neurons/physiology , Primary Visual Cortex/physiology , Visual Perception , Animals , Arousal , Datasets as Topic , Female , Humans , Male , Mice , Mice, Inbred C57BL , Nerve Net , Photic Stimulation , Primary Visual Cortex/cytology , Sensory Thresholds
3.
Cell ; 184(4): 1047-1063.e23, 2021 02 18.
Article in English | MEDLINE | ID: mdl-33539780

ABSTRACT

DNA has not been utilized to record temporal information, although DNA has been used to record biological information and to compute mathematical problems. Here, we found that indel generation by Cas9 and guide RNA can occur at steady rates, in contrast to typical dynamic biological reactions, and the accumulated indel frequency can be a function of time. By measuring indel frequencies, we developed a method for recording and measuring absolute time periods over hours to weeks in mammalian cells. These time-recordings were conducted in several cell types, with different promoters and delivery vectors for Cas9, and in both cultured cells and cells of living mice. As applications, we recorded the duration of chemical exposure and the lengths of elapsed time since the onset of biological events (e.g., heat exposure and inflammation). We propose that our systems could serve as synthetic "DNA clocks."


Subject(s)
CRISPR-Associated Protein 9/metabolism , Animals , Base Sequence , Cellular Microenvironment , Computer Simulation , HEK293 Cells , Half-Life , Humans , INDEL Mutation/genetics , Inflammation/pathology , Integrases/metabolism , Male , Mice, Nude , Promoter Regions, Genetic/genetics , RNA, Guide, Kinetoplastida/genetics , Reproducibility of Results , Time Factors
4.
Annu Rev Biochem ; 86: 777-797, 2017 06 20.
Article in English | MEDLINE | ID: mdl-28654321

ABSTRACT

Severe changes in the environmental redox potential, and resulting alterations in the oxidation states of intracellular metabolites and enzymes, have historically been considered negative stressors, requiring responses that are strictly defensive. However, recent work in diverse organisms has revealed that more subtle changes in the intracellular redox state can act as signals, eliciting responses with benefits beyond defense and detoxification. Changes in redox state have been shown to influence or trigger chromosome segregation, sporulation, aerotaxis, and social behaviors, including luminescence as well as biofilm establishment and dispersal. Connections between redox state and complex behavior allow bacteria to link developmental choices with metabolic state and coordinate appropriate responses. Promising future directions for this area of study include metabolomic analysis of species- and condition-dependent changes in metabolite oxidation states and elucidation of the mechanisms whereby the redox state influences circadian regulation.


Subject(s)
Biofilms/growth & development , Escherichia coli Proteins/metabolism , Gene Expression Regulation, Bacterial , Membrane Proteins/metabolism , Protein Kinases/metabolism , Protein Serine-Threonine Kinases/metabolism , Spores, Bacterial/metabolism , Aliivibrio fischeri/genetics , Aliivibrio fischeri/growth & development , Aliivibrio fischeri/metabolism , Bacillus subtilis/genetics , Bacillus subtilis/growth & development , Bacillus subtilis/metabolism , Caulobacter crescentus/genetics , Caulobacter crescentus/growth & development , Caulobacter crescentus/metabolism , Escherichia coli/genetics , Escherichia coli/growth & development , Escherichia coli/metabolism , Escherichia coli Proteins/genetics , Glutathione/metabolism , Membrane Proteins/genetics , Oxidation-Reduction , Protein Kinases/genetics , Protein Serine-Threonine Kinases/genetics , Pseudomonas aeruginosa/genetics , Pseudomonas aeruginosa/growth & development , Pseudomonas aeruginosa/metabolism , Signal Transduction , Spores, Bacterial/genetics , Spores, Bacterial/growth & development , Streptomyces/genetics , Streptomyces/growth & development , Streptomyces/metabolism
5.
Immunity ; 54(5): 916-930.e7, 2021 05 11.
Article in English | MEDLINE | ID: mdl-33979588

ABSTRACT

Macrophages initiate inflammatory responses via the transcription factor NFκB. The temporal pattern of NFκB activity determines which genes are expressed and thus, the type of response that ensues. Here, we examined how information about the stimulus is encoded in the dynamics of NFκB activity. We generated an mVenus-RelA reporter mouse line to enable high-throughput live-cell analysis of primary macrophages responding to host- and pathogen-derived stimuli. An information-theoretic workflow identified six dynamical features-termed signaling codons-that convey stimulus information to the nucleus. In particular, oscillatory trajectories were a hallmark of responses to cytokine but not pathogen-derived stimuli. Single-cell imaging and RNA sequencing of macrophages from a mouse model of Sjögren's syndrome revealed inappropriate responses to stimuli, suggestive of confusion of two NFκB signaling codons. Thus, the dynamics of NFκB signaling classify immune threats through six signaling codons, and signal confusion based on defective codon deployment may underlie the etiology of some inflammatory diseases.


Subject(s)
Codon/genetics , Macrophages/physiology , NF-kappa B/genetics , Signal Transduction/genetics , Animals , Cells, Cultured , Cytokines/genetics , Disease Models, Animal , Gene Expression Regulation/genetics , Inflammation/genetics , Mice , Mice, Inbred C57BL , Sjogren's Syndrome/genetics , Transcription Factor RelA/genetics
6.
Annu Rev Cell Dev Biol ; 31: 1-9, 2015.
Article in English | MEDLINE | ID: mdl-26393774

ABSTRACT

I am a developmental biologist, but I started off as a civil engineer. I did some research on soil mechanics but decided to change to biology. A friend changed my life when he told me about the mechanics of cell division, on which I did my PhD at Kings College. I then worked on the morphogenesis of the sea urchin embryo and became interested in how embryos are patterned, and I proposed positional information as a basic mechanism. I was a professor at the Middlesex Hospital Medical School, where we concentrated on how the chick limb developed.


Subject(s)
Morphogenesis/physiology , Animals , Chickens/growth & development , Developmental Biology/methods , Sea Urchins/embryology
7.
Trends Biochem Sci ; 49(10): 846-858, 2024 Oct.
Article in English | MEDLINE | ID: mdl-39004583

ABSTRACT

The poly(A) tail is an essential structural component of mRNA required for the latter's stability and translation. Recent technologies have enabled transcriptome-wide profiling of the length and composition of poly(A) tails, shedding light on their overlooked regulatory capacities. Notably, poly(A) tails contain not only adenine but also uracil, cytosine, and guanine residues. These findings strongly suggest that poly(A) tails could encode a wealth of regulatory information, similar to known reversible RNA chemical modifications. This review aims to succinctly summarize our current knowledge on the composition, dynamics, and regulatory functions of RNA poly(A) tails. Given their capacity to carry rich regulatory information beyond the genetic code, we propose the concept of 'poly(A) tail epigenetic information' as a new layer of RNA epigenetic regulation.


Subject(s)
Epigenesis, Genetic , Poly A , Humans , Poly A/metabolism , Poly A/chemistry , RNA/metabolism , RNA/chemistry , RNA/genetics , Animals , RNA, Messenger/genetics , RNA, Messenger/metabolism , RNA, Messenger/chemistry
8.
Proc Natl Acad Sci U S A ; 121(30): e2315438121, 2024 Jul 23.
Article in English | MEDLINE | ID: mdl-39028693

ABSTRACT

There is evidence from both behavior and brain activity that the way information is structured, through the use of focus, can up-regulate processing of focused constituents, likely to give prominence to the relevant aspects of the input. This is hypothesized to be universal, regardless of the different ways in which languages encode focus. In order to test this universalist hypothesis, we need to go beyond the more familiar linguistic strategies for marking focus, such as by means of intonation or specific syntactic structures (e.g., it-clefts). Therefore, in this study, we examine Makhuwa-Enahara, a Bantu language spoken in northern Mozambique, which uniquely marks focus through verbal conjugation. The participants were presented with sentences that consisted of either a semantically anomalous constituent or a semantically nonanomalous constituent. Moreover, focus on this particular constituent could be either present or absent. We observed a consistent pattern: Focused information generated a more negative N400 response than the same information in nonfocus position. This demonstrates that regardless of how focus is marked, its consequence seems to result in an upregulation of processing of information that is in focus.


Subject(s)
Language , Humans , Female , Male , Adult , Mozambique , Electroencephalography , Semantics , Brain/physiology , Young Adult , Linguistics , Evoked Potentials/physiology
9.
Proc Natl Acad Sci U S A ; 121(42): e2408696121, 2024 Oct 15.
Article in English | MEDLINE | ID: mdl-39374400

ABSTRACT

A key challenge in molecular biology is to decipher the mapping of protein sequence to function. To perform this mapping requires the identification of sequence features most informative about function. Here, we quantify the amount of information (in bits) that T cell receptor (TCR) sequence features provide about antigen specificity. We identify informative features by their degree of conservation among antigen-specific receptors relative to null expectations. We find that TCR specificity synergistically depends on the hypervariable regions of both receptor chains, with a degree of synergy that strongly depends on the ligand. Using a coincidence-based approach to measuring information enables us to directly bound the accuracy with which TCR specificity can be predicted from partial matches to reference sequences. We anticipate that our statistical framework will be of use for developing machine learning models for TCR specificity prediction and for optimizing TCRs for cell therapies. The proposed coincidence-based information measures might find further applications in bounding the performance of pairwise classifiers in other fields.


Subject(s)
Receptors, Antigen, T-Cell , T-Lymphocytes , Receptors, Antigen, T-Cell/immunology , Receptors, Antigen, T-Cell/metabolism , Receptors, Antigen, T-Cell/genetics , Humans , T-Lymphocytes/immunology , T-Lymphocytes/metabolism , Animals , T-Cell Antigen Receptor Specificity , Amino Acid Sequence
10.
Proc Natl Acad Sci U S A ; 121(23): e2322326121, 2024 Jun 04.
Article in English | MEDLINE | ID: mdl-38819997

ABSTRACT

A key feature of many developmental systems is their ability to self-organize spatial patterns of functionally distinct cell fates. To ensure proper biological function, such patterns must be established reproducibly, by controlling and even harnessing intrinsic and extrinsic fluctuations. While the relevant molecular processes are increasingly well understood, we lack a principled framework to quantify the performance of such stochastic self-organizing systems. To that end, we introduce an information-theoretic measure for self-organized fate specification during embryonic development. We show that the proposed measure assesses the total information content of fate patterns and decomposes it into interpretable contributions corresponding to the positional and correlational information. By optimizing the proposed measure, our framework provides a normative theory for developmental circuits, which we demonstrate on lateral inhibition, cell type proportioning, and reaction-diffusion models of self-organization. This paves a way toward a classification of developmental systems based on a common information-theoretic language, thereby organizing the zoo of implicated chemical and mechanical signaling processes.


Subject(s)
Models, Biological , Animals , Embryonic Development
11.
Proc Natl Acad Sci U S A ; 121(2): e2313754120, 2024 Jan 09.
Article in English | MEDLINE | ID: mdl-38165926

ABSTRACT

Controlled interaction between localized and delocalized solid-state spin systems offers a compelling platform for on-chip quantum information processing with quantum spintronics. Hybrid quantum systems (HQSs) of localized nitrogen-vacancy (NV) centers in diamond and delocalized magnon modes in ferrimagnets-systems with naturally commensurate energies-have recently attracted significant attention, especially for interconnecting isolated spin qubits at length-scales far beyond those set by the dipolar coupling. However, despite extensive theoretical efforts, there is a lack of experimental characterization of the magnon-mediated interaction between NV centers, which is necessary to develop such hybrid quantum architectures. Here, we experimentally determine the magnon-mediated NV-NV coupling from the magnon-induced self-energy of NV centers. Our results are quantitatively consistent with a model in which the NV center is coupled to magnons by dipolar interactions. This work provides a versatile tool to characterize HQSs in the absence of strong coupling, informing future efforts to engineer entangled solid-state systems.

12.
Proc Natl Acad Sci U S A ; 121(10): e2315195121, 2024 Mar 05.
Article in English | MEDLINE | ID: mdl-38412133

ABSTRACT

A great deal of empirical research has examined who falls for misinformation and why. Here, we introduce a formal game-theoretic model of engagement with news stories that captures the strategic interplay between (mis)information consumers and producers. A key insight from the model is that observed patterns of engagement do not necessarily reflect the preferences of consumers. This is because producers seeking to promote misinformation can use strategies that lead moderately inattentive readers to engage more with false stories than true ones-even when readers prefer more accurate over less accurate information. We then empirically test people's preferences for accuracy in the news. In three studies, we find that people strongly prefer to click and share news they perceive as more accurate-both in a general population sample, and in a sample of users recruited through Twitter who had actually shared links to misinformation sites online. Despite this preference for accurate news-and consistent with the predictions of our model-we find markedly different engagement patterns for articles from misinformation versus mainstream news sites. Using 1,000 headlines from 20 misinformation and 20 mainstream news sites, we compare Facebook engagement data with 20,000 accuracy ratings collected in a survey experiment. Engagement with a headline is negatively correlated with perceived accuracy for misinformation sites, but positively correlated with perceived accuracy for mainstream sites. Taken together, these theoretical and empirical results suggest that consumer preferences cannot be straightforwardly inferred from empirical patterns of engagement.


Subject(s)
Consumer Behavior , Social Media , Humans , Communication , Surveys and Questionnaires , Cognition , Empirical Research
13.
Proc Natl Acad Sci U S A ; 121(12): e2310002121, 2024 Mar 19.
Article in English | MEDLINE | ID: mdl-38470929

ABSTRACT

We develop information-geometric techniques to analyze the trajectories of the predictions of deep networks during training. By examining the underlying high-dimensional probabilistic models, we reveal that the training process explores an effectively low-dimensional manifold. Networks with a wide range of architectures, sizes, trained using different optimization methods, regularization techniques, data augmentation techniques, and weight initializations lie on the same manifold in the prediction space. We study the details of this manifold to find that networks with different architectures follow distinguishable trajectories, but other factors have a minimal influence; larger networks train along a similar manifold as that of smaller networks, just faster; and networks initialized at very different parts of the prediction space converge to the solution along a similar manifold.

14.
Proc Natl Acad Sci U S A ; 121(14): e2305297121, 2024 Apr 02.
Article in English | MEDLINE | ID: mdl-38551842

ABSTRACT

The causal connectivity of a network is often inferred to understand network function. It is arguably acknowledged that the inferred causal connectivity relies on the causality measure one applies, and it may differ from the network's underlying structural connectivity. However, the interpretation of causal connectivity remains to be fully clarified, in particular, how causal connectivity depends on causality measures and how causal connectivity relates to structural connectivity. Here, we focus on nonlinear networks with pulse signals as measured output, e.g., neural networks with spike output, and address the above issues based on four commonly utilized causality measures, i.e., time-delayed correlation coefficient, time-delayed mutual information, Granger causality, and transfer entropy. We theoretically show how these causality measures are related to one another when applied to pulse signals. Taking a simulated Hodgkin-Huxley network and a real mouse brain network as two illustrative examples, we further verify the quantitative relations among the four causality measures and demonstrate that the causal connectivity inferred by any of the four well coincides with the underlying network structural connectivity, therefore illustrating a direct link between the causal and structural connectivity. We stress that the structural connectivity of pulse-output networks can be reconstructed pairwise without conditioning on the global information of all other nodes in a network, thus circumventing the curse of dimensionality. Our framework provides a practical and effective approach for pulse-output network reconstruction.

15.
Proc Natl Acad Sci U S A ; 121(30): e2405451121, 2024 Jul 23.
Article in English | MEDLINE | ID: mdl-39008663

ABSTRACT

Reinforcement learning inspires much theorizing in neuroscience, cognitive science, machine learning, and AI. A central question concerns the conditions that produce the perception of a contingency between an action and reinforcement-the assignment-of-credit problem. Contemporary models of associative and reinforcement learning do not leverage the temporal metrics (measured intervals). Our information-theoretic approach formalizes contingency by time-scale invariant temporal mutual information. It predicts that learning may proceed rapidly even with extremely long action-reinforcer delays. We show that rats can learn an action after a single reinforcement, even with a 16-min delay between the action and reinforcement (15-fold longer than any delay previously shown to support such learning). By leveraging metric temporal information, our solution obviates the need for windows of associability, exponentially decaying eligibility traces, microstimuli, or distributions over Bayesian belief states. Its three equations have no free parameters; they predict one-shot learning without iterative simulation.


Subject(s)
Reinforcement, Psychology , Animals , Rats , Learning/physiology , Time Factors , Bayes Theorem
16.
Proc Natl Acad Sci U S A ; 121(6): e2312521121, 2024 Feb 06.
Article in English | MEDLINE | ID: mdl-38285940

ABSTRACT

Microbial systems appear to exhibit a relatively high switching capacity of moving back and forth among few dominant communities (taxon memberships). While this switching behavior has been mainly attributed to random environmental factors, it remains unclear the extent to which internal community dynamics affect the switching capacity of microbial systems. Here, we integrate ecological theory and empirical data to demonstrate that structured community transitions increase the dependency of future communities on the current taxon membership, enhancing the switching capacity of microbial systems. Following a structuralist approach, we propose that each community is feasible within a unique domain in environmental parameter space. Then, structured transitions between any two communities can happen with probability proportional to the size of their feasibility domains and inversely proportional to their distance in environmental parameter space-which can be treated as a special case of the gravity model. We detect two broad classes of systems with structured transitions: one class where switching capacity is high across a wide range of community sizes and another class where switching capacity is high only inside a narrow size range. We corroborate our theory using temporal data of gut and oral microbiota (belonging to class 1) as well as vaginal and ocean microbiota (belonging to class 2). These results reveal that the topology of feasibility domains in environmental parameter space is a relevant property to understand the changing behavior of microbial systems. This knowledge can be potentially used to understand the relevant community size at which internal dynamics can be operating in microbial systems.


Subject(s)
Ecology , Environment , Microbiota
17.
Proc Natl Acad Sci U S A ; 121(24): e2311241121, 2024 Jun 11.
Article in English | MEDLINE | ID: mdl-38838020

ABSTRACT

We present the experimental finding of multiple simultaneous two-fold degeneracies in the spectrum of a Kerr oscillator subjected to a squeezing drive. This squeezing drive resulting from a three-wave mixing process, in combination with the Kerr interaction, creates an effective static two-well potential in the phase space rotating at half the frequency of the sinusoidal drive generating the squeezing. Remarkably, these degeneracies can be turned on-and-off on demand, as well as their number by simply adjusting the frequency of the squeezing drive. We find that when the detuning Δ between the frequency of the oscillator and the second subharmonic of the drive equals an even multiple of the Kerr coefficient K, [Formula: see text], the oscillator displays [Formula: see text] exact, parity-protected, spectral degeneracies, insensitive to the drive amplitude. These degeneracies can be explained by the unusual destructive interference of tunnel paths in the classically forbidden region of the double well static effective potential that models our experiment. Exploiting this interference, we measure a peaked enhancement of the incoherent well-switching lifetime, thus creating a protected cat qubit in the ground state manifold of our oscillator. Our results illustrate the relationship between degeneracies and noise protection in a driven quantum system.

18.
Proc Natl Acad Sci U S A ; 121(35): e2400082121, 2024 Aug 27.
Article in English | MEDLINE | ID: mdl-39178232

ABSTRACT

To efficiently yet reliably represent and process information, our brains need to produce information-rich signals that differentiate between moments or cognitive states, while also being robust to noise or corruption. For many, though not all, natural systems, these two properties are often inversely related: More information-rich signals are less robust, and vice versa. Here, we examined how these properties change with ongoing cognitive demands. To this end, we applied dimensionality reduction algorithms and pattern classifiers to functional neuroimaging data collected as participants listened to a story, temporally scrambled versions of the story, or underwent a resting state scanning session. We considered two primary aspects of the neural data recorded in these different experimental conditions. First, we treated the maximum achievable decoding accuracy across participants as an indicator of the "informativeness" of the recorded patterns. Second, we treated the number of features (components) required to achieve a threshold decoding accuracy as a proxy for the "compressibility" of the neural patterns (where fewer components indicate greater compression). Overall, we found that the peak decoding accuracy (achievable without restricting the numbers of features) was highest in the intact (unscrambled) story listening condition. However, the number of features required to achieve comparable classification accuracy was also lowest in the intact story listening condition. Taken together, our work suggests that our brain networks flexibly reconfigure according to ongoing task demands and that the activity patterns associated with higher-order cognition and high engagement are both more informative and more compressible than the activity patterns associated with lower-order tasks and lower engagement.


Subject(s)
Brain , Cognition , Magnetic Resonance Imaging , Humans , Cognition/physiology , Brain/physiology , Brain/diagnostic imaging , Male , Female , Adult , Magnetic Resonance Imaging/methods , Brain Mapping/methods , Young Adult , Algorithms
19.
Proc Natl Acad Sci U S A ; 121(25): e2312293121, 2024 Jun 18.
Article in English | MEDLINE | ID: mdl-38857385

ABSTRACT

The perception of sensory attributes is often quantified through measurements of sensitivity (the ability to detect small stimulus changes), as well as through direct judgments of appearance or intensity. Despite their ubiquity, the relationship between these two measurements remains controversial and unresolved. Here, we propose a framework in which they arise from different aspects of a common representation. Specifically, we assume that judgments of stimulus intensity (e.g., as measured through rating scales) reflect the mean value of an internal representation, and sensitivity reflects a combination of mean value and noise properties, as quantified by the statistical measure of Fisher information. Unique identification of these internal representation properties can be achieved by combining measurements of sensitivity and judgments of intensity. As a central example, we show that Weber's law of perceptual sensitivity can coexist with Stevens' power-law scaling of intensity ratings (for all exponents), when the noise amplitude increases in proportion to the representational mean. We then extend this result beyond the Weber's law range by incorporating a more general and physiology-inspired form of noise and show that the combination of noise properties and sensitivity measurements accurately predicts intensity ratings across a variety of sensory modalities and attributes. Our framework unifies two primary perceptual measurements-thresholds for sensitivity and rating scales for intensity-and provides a neural interpretation for the underlying representation.


Subject(s)
Perception , Humans , Perception/physiology , Sensory Thresholds/physiology , Sensation/physiology , Judgment/physiology
20.
Proc Natl Acad Sci U S A ; 121(13): e2312988121, 2024 Mar 26.
Article in English | MEDLINE | ID: mdl-38498714

ABSTRACT

One of the fundamental steps toward understanding a complex system is identifying variation at the scale of the system's components that is most relevant to behavior on a macroscopic scale. Mutual information provides a natural means of linking variation across scales of a system due to its independence of functional relationship between observables. However, characterizing the manner in which information is distributed across a set of observables is computationally challenging and generally infeasible beyond a handful of measurements. Here, we propose a practical and general methodology that uses machine learning to decompose the information contained in a set of measurements by jointly optimizing a lossy compression of each measurement. Guided by the distributed information bottleneck as a learning objective, the information decomposition identifies the variation in the measurements of the system state most relevant to specified macroscale behavior. We focus our analysis on two paradigmatic complex systems: a Boolean circuit and an amorphous material undergoing plastic deformation. In both examples, the large amount of entropy of the system state is decomposed, bit by bit, in terms of what is most related to macroscale behavior. The identification of meaningful variation in data, with the full generality brought by information theory, is made practical for studying the connection between micro- and macroscale structure in complex systems.

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