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Brückner DB, Tkačik G. Information content and optimization of self-organized developmental systems. Proc Natl Acad Sci U S A 2024; 121:e2322326121. [PMID: 38819997 PMCID: PMC11161761 DOI: 10.1073/pnas.2322326121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/18/2023] [Accepted: 04/27/2024] [Indexed: 06/02/2024] Open
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.
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Affiliation(s)
- David B. Brückner
- Institute of Science and Technology Austria, AT-3400Klosterneuburg, Austria
| | - Gašper Tkačik
- Institute of Science and Technology Austria, AT-3400Klosterneuburg, Austria
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2
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Tjalma AJ, Galstyan V, Goedhart J, Slim L, Becker NB, ten Wolde PR. Trade-offs between cost and information in cellular prediction. Proc Natl Acad Sci U S A 2023; 120:e2303078120. [PMID: 37792515 PMCID: PMC10576116 DOI: 10.1073/pnas.2303078120] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/23/2023] [Accepted: 08/23/2023] [Indexed: 10/06/2023] Open
Abstract
Living cells can leverage correlations in environmental fluctuations to predict the future environment and mount a response ahead of time. To this end, cells need to encode the past signal into the output of the intracellular network from which the future input is predicted. Yet, storing information is costly while not all features of the past signal are equally informative on the future input signal. Here, we show for two classes of input signals that cellular networks can reach the fundamental bound on the predictive information as set by the information extracted from the past signal: Push-pull networks can reach this information bound for Markovian signals, while networks that take a temporal derivative can reach the bound for predicting the future derivative of non-Markovian signals. However, the bits of past information that are most informative about the future signal are also prohibitively costly. As a result, the optimal system that maximizes the predictive information for a given resource cost is, in general, not at the information bound. Applying our theory to the chemotaxis network of Escherichia coli reveals that its adaptive kernel is optimal for predicting future concentration changes over a broad range of background concentrations, and that the system has been tailored to predicting these changes in shallow gradients.
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Affiliation(s)
- Age J. Tjalma
- AMOLF, Science Park 104, 1098 XGAmsterdam, The Netherlands
| | - Vahe Galstyan
- AMOLF, Science Park 104, 1098 XGAmsterdam, The Netherlands
| | | | - Lotte Slim
- AMOLF, Science Park 104, 1098 XGAmsterdam, The Netherlands
| | - Nils B. Becker
- Theoretical Systems Biology, German Cancer Research Center, 69120Heidelberg, Germany
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Thompson MJ, Young CA, Munnamalai V, Umulis DM. Early radial positional information in the cochlea is optimized by a precise linear BMP gradient and enhanced by SOX2. Sci Rep 2023; 13:8567. [PMID: 37237002 PMCID: PMC10219982 DOI: 10.1038/s41598-023-34725-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/23/2023] [Accepted: 05/06/2023] [Indexed: 05/28/2023] Open
Abstract
Positional information encoded in signaling molecules is essential for early patterning in the prosensory domain of the developing cochlea. The sensory epithelium, the organ of Corti, contains an exquisite repeating pattern of hair cells and supporting cells. This requires precision in the morphogen signals that set the initial radial compartment boundaries, but this has not been investigated. To measure gradient formation and morphogenetic precision in developing cochlea, we developed a quantitative image analysis procedure measuring SOX2 and pSMAD1/5/9 profiles in mouse embryos at embryonic day (E)12.5, E13.5, and E14.5. Intriguingly, we found that the pSMAD1/5/9 profile forms a linear gradient up to the medial ~ 75% of the PSD from the pSMAD1/5/9 peak in the lateral edge during E12.5 and E13.5. This is a surprising activity readout for a diffusive BMP4 ligand secreted from a tightly constrained lateral region since morphogens typically form exponential or power-law gradient shapes. This is meaningful for gradient interpretation because while linear profiles offer the theoretically highest information content and distributed precision for patterning, a linear morphogen gradient has not yet been observed. Furthermore, this is unique to the cochlear epithelium as the pSMAD1/5/9 gradient is exponential in the surrounding mesenchyme. In addition to the information-optimized linear profile, we found that while pSMAD1/5/9 is stable during this timeframe, an accompanying gradient of SOX2 shifts dynamically. Last, through joint decoding maps of pSMAD1/5/9 and SOX2, we see that there is a high-fidelity mapping between signaling activity and position in the regions that will become Kölliker's organ and the organ of Corti. Mapping is ambiguous in the prosensory domain precursory to the outer sulcus. Altogether, this research provides new insights into the precision of early morphogenetic patterning cues in the radial cochlea prosensory domain.
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Affiliation(s)
- Matthew J Thompson
- Weldon School of Biomedical Engineering, Purdue University, 206 S Martin Jischke Dr, West Lafayette, IN, 47907, USA
| | - Caryl A Young
- University of Maine, 168 College Ave, Orono, ME, 04469, USA
| | - Vidhya Munnamalai
- University of Maine, 168 College Ave, Orono, ME, 04469, USA.
- The Jackson Laboratory, 600 Main Street, Bar Harbor, ME, 04609, USA.
| | - David M Umulis
- Weldon School of Biomedical Engineering, Purdue University, 206 S Martin Jischke Dr, West Lafayette, IN, 47907, USA.
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François P. New wave theory. Development 2023; 150:287679. [PMID: 36815628 DOI: 10.1242/dev.201647] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/24/2023]
Affiliation(s)
- Paul François
- Department of Biochemistry, Université de Montréal, Montréal, Quebec H3T 1J4, Canada
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Saha S, Moon HR, Han B, Mugler A. Deduction of signaling mechanisms from cellular responses to multiple cues. NPJ Syst Biol Appl 2022; 8:48. [PMID: 36450797 PMCID: PMC9712676 DOI: 10.1038/s41540-022-00262-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/16/2022] [Accepted: 11/08/2022] [Indexed: 12/05/2022] Open
Abstract
Cell signaling networks are complex and often incompletely characterized, making it difficult to obtain a comprehensive picture of the mechanisms they encode. Mathematical modeling of these networks provides important clues, but the models themselves are often complex, and it is not always clear how to extract falsifiable predictions. Here we take an inverse approach, using experimental data at the cell level to deduce the minimal signaling network. We focus on cells' response to multiple cues, specifically on the surprising case in which the response is antagonistic: the response to multiple cues is weaker than the response to the individual cues. We systematically build candidate signaling networks one node at a time, using the ubiquitous ingredients of (i) up- or down-regulation, (ii) molecular conversion, or (iii) reversible binding. In each case, our method reveals a minimal, interpretable signaling mechanism that explains the antagonistic response. Our work provides a systematic way to deduce molecular mechanisms from cell-level data.
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Affiliation(s)
- Soutick Saha
- grid.169077.e0000 0004 1937 2197Department of Physics and Astronomy, Purdue University, West Lafayette, IN 47907 USA
| | - Hye-ran Moon
- grid.169077.e0000 0004 1937 2197School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907 USA
| | - Bumsoo Han
- grid.169077.e0000 0004 1937 2197School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907 USA ,grid.169077.e0000 0004 1937 2197Purdue Center for Cancer Research, Purdue University, West Lafayette, IN 47907 USA
| | - Andrew Mugler
- grid.169077.e0000 0004 1937 2197Department of Physics and Astronomy, Purdue University, West Lafayette, IN 47907 USA ,grid.169077.e0000 0004 1937 2197Purdue Center for Cancer Research, Purdue University, West Lafayette, IN 47907 USA ,grid.21925.3d0000 0004 1936 9000Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA 15260 USA
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How does an organism extract relevant information from transcription factor concentrations? Biochem Soc Trans 2022; 50:1365-1376. [DOI: 10.1042/bst20220333] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2022] [Revised: 08/16/2022] [Accepted: 08/17/2022] [Indexed: 11/17/2022]
Abstract
How does an organism regulate its genes? The involved regulation typically occurs in terms of a signal processing chain: an externally applied stimulus or a maternally supplied transcription factor leads to the expression of some downstream genes, which, in turn, are transcription factors for further genes. Especially during development, these transcription factors are frequently expressed in amounts where noise is still important; yet, the signals that they provide must not be lost in the noise. Thus, the organism needs to extract exactly relevant information in the signal. New experimental approaches involving single-molecule measurements at high temporal precision as well as increased precision in manipulations directly on the genome are allowing us to tackle this question anew. These new experimental advances mean that also from the theoretical side, theoretical advances should be possible. In this review, I will describe, specifically on the example of fly embryo gene regulation, how theoretical approaches, especially from inference and information theory, can help in understanding gene regulation. To do so, I will first review some more traditional theoretical models for gene regulation, followed by a brief discussion of information-theoretical approaches and when they can be applied. I will then introduce early fly development as an exemplary system where such information-theoretical approaches have traditionally been applied and can be applied; I will specifically focus on how one such method, namely the information bottleneck approach, has recently been used to infer structural features of enhancer architecture.
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Latent space of a small genetic network: Geometry of dynamics and information. Proc Natl Acad Sci U S A 2022; 119:e2113651119. [PMID: 35737842 PMCID: PMC9245618 DOI: 10.1073/pnas.2113651119] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2023] Open
Abstract
The high-dimensional character of most biological systems presents genuine challenges for modeling and prediction. Here we propose a neural network-based approach for dimensionality reduction and analysis of biological gene expression data, using, as a case study, a well-known genetic network in the early Drosophila embryo, the gap gene patterning system. We build an autoencoder compressing the dynamics of spatial gap gene expression into a two-dimensional (2D) latent map. The resulting 2D dynamics suggests an almost linear model, with a small bare set of essential interactions. Maternally defined spatial modes control gap genes positioning, without the classically assumed intricate set of repressive gap gene interactions. This, surprisingly, predicts minimal changes of neighboring gap domains when knocking out gap genes, consistent with previous observations. Latent space geometries in maternal mutants are also consistent with the existence of such spatial modes. Finally, we show how positional information is well defined and interpretable as a polar angle in latent space. Our work illustrates how optimization of small neural networks on medium-sized biological datasets is sufficiently informative to capture essential underlying mechanisms of network function.
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Achar SR, Bourassa FXP, Rademaker TJ, Lee A, Kondo T, Salazar-Cavazos E, Davies JS, Taylor N, François P, Altan-Bonnet G. Universal antigen encoding of T cell activation from high-dimensional cytokine dynamics. Science 2022; 376:880-884. [PMID: 35587980 DOI: 10.1126/science.abl5311] [Citation(s) in RCA: 23] [Impact Index Per Article: 11.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
Abstract
Systems immunology lacks a framework with which to derive theoretical understanding from high-dimensional datasets. We combined a robotic platform with machine learning to experimentally measure and theoretically model CD8+ T cell activation. High-dimensional cytokine dynamics could be compressed onto a low-dimensional latent space in an antigen-specific manner (so-called "antigen encoding"). We used antigen encoding to model and reconstruct patterns of T cell immune activation. The model delineated six classes of antigens eliciting distinct T cell responses. We generalized antigen encoding to multiple immune settings, including drug perturbations and activation of chimeric antigen receptor T cells. Such universal antigen encoding for T cell activation may enable further modeling of immune responses and their rational manipulation to optimize immunotherapies.
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Affiliation(s)
- Sooraj R Achar
- Immunodynamics Group, Laboratory of Integrative Cancer Immunology, Center for Cancer Research, National Cancer Institute, Bethesda, MD, USA
| | | | | | - Angela Lee
- Immunodynamics Group, Laboratory of Integrative Cancer Immunology, Center for Cancer Research, National Cancer Institute, Bethesda, MD, USA
| | - Taisuke Kondo
- Pediatric Oncology Branch, Center for Cancer Research, National Cancer Institute, Bethesda, MD, USA
| | - Emanuel Salazar-Cavazos
- Immunodynamics Group, Laboratory of Integrative Cancer Immunology, Center for Cancer Research, National Cancer Institute, Bethesda, MD, USA
| | - John S Davies
- Genitourinary Malignancies Branch, Center for Cancer Research, National Cancer Institute, Bethesda, MD, USA
| | - Naomi Taylor
- Pediatric Oncology Branch, Center for Cancer Research, National Cancer Institute, Bethesda, MD, USA
| | - Paul François
- Department of Physics, McGill University, Montréal, Québec, Canada
| | - Grégoire Altan-Bonnet
- Immunodynamics Group, Laboratory of Integrative Cancer Immunology, Center for Cancer Research, National Cancer Institute, Bethesda, MD, USA
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Lacalli TC. Patterning, From Conifers to Consciousness: Turing’s Theory and Order From Fluctuations. Front Cell Dev Biol 2022; 10:871950. [PMID: 35592249 PMCID: PMC9111979 DOI: 10.3389/fcell.2022.871950] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/08/2022] [Accepted: 03/11/2022] [Indexed: 11/19/2022] Open
Abstract
This is a brief account of Turing’s ideas on biological pattern and the events that led to their wider acceptance by biologists as a valid way to investigate developmental pattern, and of the value of theory more generally in biology. Periodic patterns have played a key role in this process, especially 2D arrays of oriented stripes, which proved a disappointment in theoretical terms in the case of Drosophila segmentation, but a boost to theory as applied to skin patterns in fish and model chemical reactions. The concept of “order from fluctuations” is a key component of Turing’s theory, wherein pattern arises by selective amplification of spatial components concealed in the random disorder of molecular and/or cellular processes. For biological examples, a crucial point from an analytical standpoint is knowing the nature of the fluctuations, where the amplifier resides, and the timescale over which selective amplification occurs. The answer clarifies the difference between “inelegant” examples such as Drosophila segmentation, which is perhaps better understood as a programmatic assembly process, and “elegant” ones expressible in equations like Turing’s: that the fluctuations and selection process occur predominantly in evolutionary time for the former, but in real time for the latter, and likewise for error suppression, which for Drosophila is historical, in being lodged firmly in past evolutionary events. The prospects for a further extension of Turing’s ideas to the complexities of brain development and consciousness is discussed, where a case can be made that it could well be in neuroscience that his ideas find their most important application.
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