1
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Long Y, Vetter R, Iber D. 2D effects enhance precision of gradient-based tissue patterning. iScience 2023; 26:107880. [PMID: 37810247 PMCID: PMC10550716 DOI: 10.1016/j.isci.2023.107880] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/27/2023] [Revised: 06/26/2023] [Accepted: 09/07/2023] [Indexed: 10/10/2023] Open
Abstract
Robust embryonic development requires pattern formation with high spatial accuracy. In epithelial tissues that are patterned by morphogen gradients, the emerging patterns achieve levels of precision that have recently been explained by a simple one-dimensional reaction-diffusion model with kinetic noise. Here, we show that patterning precision is even greater if transverse diffusion effects are at play in such tissues. The positional error, a measure for spatial patterning accuracy, decreases in wider tissues but then saturates beyond a width of about ten cells. This demonstrates that the precision of gradient-based patterning in two- or higher-dimensional systems can be even greater than predicted by 1D models, and further attests to the potential of noisy morphogen gradients for high-precision tissue patterning.
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Affiliation(s)
- Yuchong Long
- Department of Biosystems Science and Engineering, ETH Zürich, Mattenstrasse 26, 4058 Basel, Switzerland
| | - Roman Vetter
- Department of Biosystems Science and Engineering, ETH Zürich, Mattenstrasse 26, 4058 Basel, Switzerland
- Swiss Institute of Bioinformatics, Mattenstrasse 26, 4058 Basel, Switzerland
| | - Dagmar Iber
- Department of Biosystems Science and Engineering, ETH Zürich, Mattenstrasse 26, 4058 Basel, Switzerland
- Swiss Institute of Bioinformatics, Mattenstrasse 26, 4058 Basel, Switzerland
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2
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Wang ZJ, Thomson M. Localization of signaling receptors maximizes cellular information acquisition in spatially structured natural environments. Cell Syst 2022; 13:530-546.e12. [PMID: 35679857 DOI: 10.1016/j.cels.2022.05.004] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/05/2021] [Revised: 02/08/2022] [Accepted: 05/12/2022] [Indexed: 01/25/2023]
Abstract
Cells in natural environments, such as tissue or soil, sense and respond to extracellular ligands with intricately structured and non-monotonic spatial distributions, sculpted by processes such as fluid flow and substrate adhesion. In this work, we show that spatial sensing and navigation can be optimized by adapting the spatial organization of signaling pathways to the spatial structure of the environment. We develop an information-theoretic framework for computing the optimal spatial organization of a sensing system for a given signaling environment. We find that receptor localization previously observed in cells maximizes information acquisition in simulated natural contexts, including tissue and soil. Specifically, information acquisition is maximized when receptors form localized patches at regions of maximal ligand concentration. Receptor localization extends naturally to produce a dynamic protocol for continuously redistributing signaling receptors, which when implemented using simple feedback, boosts cell navigation efficiency by 30-fold.
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Affiliation(s)
- Zitong Jerry Wang
- Division of Biology and Biological Engineering, California Institute of Technology, Pasadena, CA 91125, USA.
| | - Matt Thomson
- Division of Biology and Biological Engineering, California Institute of Technology, Pasadena, CA 91125, USA.
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3
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Information theory entering soils and tissues. Cell Syst 2022; 13:511-513. [PMID: 35863325 DOI: 10.1016/j.cels.2022.06.004] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/25/2023]
Abstract
For a long time, application of information theory for characterizing biological signaling fidelity was limited to "telegraph-like" situations, copying the classical scenario for which it was developed. A study published in this issue of Cell Systems applies this powerful framework to several distinct cases of dynamic signal sensing in complex geometries.
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4
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Abstract
Half a century after Lewis Wolpert's seminal conceptual advance on how cellular fates distribute in space, we provide a brief historical perspective on how the concept of positional information emerged and influenced the field of developmental biology and beyond. We focus on a modern interpretation of this concept in terms of information theory, largely centered on its application to cell specification in the early Drosophila embryo. We argue that a true physical variable (position) is encoded in local concentrations of patterning molecules, that this mapping is stochastic, and that the processes by which positions and corresponding cell fates are determined based on these concentrations need to take such stochasticity into account. With this approach, we shift the focus from biological mechanisms, molecules, genes and pathways to quantitative systems-level questions: where does positional information reside, how it is transformed and accessed during development, and what fundamental limits it is subject to?
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Affiliation(s)
- Gašper Tkačik
- Institute of Science and Technology Austria, Am Campus 1, AT-3400 Klosterneuburg, Austria
| | - Thomas Gregor
- Joseph Henry Laboratories of Physics and the Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, NJ 08544, USA
- Department of Developmental and Stem Cell Biology, UMR3738, Institut Pasteur, FR-75015 Paris, France
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5
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Jaeger J, Verd B. Dynamic positional information: Patterning mechanism versus precision in gradient-driven systems. Curr Top Dev Biol 2019; 137:219-246. [PMID: 32143744 DOI: 10.1016/bs.ctdb.2019.11.017] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022]
Abstract
There is much talk about information in biology. In developmental biology, this takes the form of "positional information," especially in the context of morphogen-based pattern formation. Unfortunately, the concept of "information" is rarely defined in any precise manner. Here, we provide two alternative interpretations of "positional information," and examine the complementary meanings and uses of each concept. Positional information defined as Shannon information helps us understand decoding and error propagation in patterning systems. General relativistic positional information, in contrast, provides a metric to assess the output of pattern-forming mechanisms. Both interpretations provide powerful conceptual tools that do not compete, but are best used in combination to gain a proper mechanistic understanding of robust patterning.
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Affiliation(s)
- Johannes Jaeger
- Complexity Science Hub (CSH), Vienna, Austria; Department of Molecular Evolution & Development, University of Vienna, Vienna, Austria.
| | - Berta Verd
- Department of Genetics, University of Cambridge, Cambridge, United Kingdom
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6
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Abstract
In order to respond to environmental signals, cells often use small molecular circuits to transmit information about their surroundings. Recently, motivated by specific examples in signaling and gene regulation, a body of work has focused on the properties of circuits that function out of equilibrium and dissipate energy. We briefly review the probabilistic measures of information and dissipation and use simple models to discuss and illustrate trade-offs between information and dissipation in biological circuits. We find that circuits with non-steady state initial conditions can transmit more information at small readout delays than steady state circuits. The dissipative cost of this additional information proves marginal compared to the steady state dissipation. Feedback does not significantly increase the transmitted information for out of steady state circuits but does decrease dissipative costs. Lastly, we discuss the case of bursty gene regulatory circuits that, even in the fast switching limit, function out of equilibrium.
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7
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Cepeda-Humerez SA, Ruess J, Tkačik G. Estimating information in time-varying signals. PLoS Comput Biol 2019; 15:e1007290. [PMID: 31479447 PMCID: PMC6743786 DOI: 10.1371/journal.pcbi.1007290] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/04/2019] [Revised: 09/13/2019] [Accepted: 07/29/2019] [Indexed: 01/16/2023] Open
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. Cells represent changes in their own state or in the state of their environment by temporally varying the concentrations of intracellular signaling molecules, mimicking in a simple chemical context the way we humans represent our thoughts and observations through temporally varying patterns of sounds that constitute speech. These time-varying concentrations are used as signals to regulate downstream molecular processes, to mount appropriate cellular responses for the environmental challenges, or to communicate with nearby cells. But how precise and unambiguous is such chemical communication, in theory and in data? On the one hand, intuition tells us that many possible environmental changes could be represented by variation in concentration patterns of multiple signaling chemicals; on the other, we know that chemical signals are inherently noisy at the molecular scale. Here we develop data analysis methodology that allows us to pose and answer these questions rigorously. Our decoding-based information estimators, which we test on simulated and real data from yeast and mammalian cells, measure how precisely individual cells can detect and report environmental changes, without making assumptions about the structure of the chemical communication and using only the amounts of data that is typically available in today’s experiments.
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Affiliation(s)
| | - Jakob Ruess
- Inria Saclay – Ile-de-France, F-91120 Palaiseau, France
- Institut Pasteur, F-75015 Paris, France
| | - Gašper Tkačik
- Institute of Science and Technology Austria, A-3400 Klosterneuburg, Austria
- * E-mail:
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8
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Sokolowski TR, Paijmans J, Bossen L, Miedema T, Wehrens M, Becker NB, Kaizu K, Takahashi K, Dogterom M, Ten Wolde PR. eGFRD in all dimensions. J Chem Phys 2019; 150:054108. [PMID: 30736681 DOI: 10.1063/1.5064867] [Citation(s) in RCA: 23] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023] Open
Abstract
Biochemical reactions often occur at low copy numbers but at once in crowded and diverse environments. Space and stochasticity therefore play an essential role in biochemical networks. Spatial-stochastic simulations have become a prominent tool for understanding how stochasticity at the microscopic level influences the macroscopic behavior of such systems. While particle-based models guarantee the level of detail necessary to accurately describe the microscopic dynamics at very low copy numbers, the algorithms used to simulate them typically imply trade-offs between computational efficiency and biochemical accuracy. eGFRD (enhanced Green's Function Reaction Dynamics) is an exact algorithm that evades such trade-offs by partitioning the N-particle system into M ≤ N analytically tractable one- and two-particle systems; the analytical solutions (Green's functions) then are used to implement an event-driven particle-based scheme that allows particles to make large jumps in time and space while retaining access to their state variables at arbitrary simulation times. Here we present "eGFRD2," a new eGFRD version that implements the principle of eGFRD in all dimensions, thus enabling efficient particle-based simulation of biochemical reaction-diffusion processes in the 3D cytoplasm, on 2D planes representing membranes, and on 1D elongated cylinders representative of, e.g., cytoskeletal tracks or DNA; in 1D, it also incorporates convective motion used to model active transport. We find that, for low particle densities, eGFRD2 is up to 6 orders of magnitude faster than conventional Brownian dynamics. We exemplify the capabilities of eGFRD2 by simulating an idealized model of Pom1 gradient formation, which involves 3D diffusion, active transport on microtubules, and autophosphorylation on the membrane, confirming recent experimental and theoretical results on this system to hold under genuinely stochastic conditions.
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Affiliation(s)
| | - Joris Paijmans
- FOM Institute AMOLF, Science Park 104, 1098 XG Amsterdam, The Netherlands
| | - Laurens Bossen
- FOM Institute AMOLF, Science Park 104, 1098 XG Amsterdam, The Netherlands
| | - Thomas Miedema
- FOM Institute AMOLF, Science Park 104, 1098 XG Amsterdam, The Netherlands
| | - Martijn Wehrens
- FOM Institute AMOLF, Science Park 104, 1098 XG Amsterdam, The Netherlands
| | - Nils B Becker
- FOM Institute AMOLF, Science Park 104, 1098 XG Amsterdam, The Netherlands
| | - Kazunari Kaizu
- Center for Biosystems Dynamics Research (BDR), RIKEN, 6-2-3 Furuedai, Suita, Osaka 565-0874, Japan
| | - Koichi Takahashi
- Center for Biosystems Dynamics Research (BDR), RIKEN, 6-2-3 Furuedai, Suita, Osaka 565-0874, Japan
| | - Marileen Dogterom
- FOM Institute AMOLF, Science Park 104, 1098 XG Amsterdam, The Netherlands
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9
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Petkova MD, Tkačik G, Bialek W, Wieschaus EF, Gregor T. Optimal Decoding of Cellular Identities in a Genetic Network. Cell 2019; 176:844-855.e15. [PMID: 30712870 DOI: 10.1016/j.cell.2019.01.007] [Citation(s) in RCA: 83] [Impact Index Per Article: 16.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/22/2018] [Revised: 11/04/2018] [Accepted: 01/02/2019] [Indexed: 11/24/2022]
Abstract
In developing organisms, spatially prescribed cell identities are thought to be determined by the expression levels of multiple genes. Quantitative tests of this idea, however, require a theoretical framework capable of exposing the rules and precision of cell specification over developmental time. We use the gap gene network in the early fly embryo as an example to show how expression levels of the four gap genes can be jointly decoded into an optimal specification of position with 1% accuracy. The decoder correctly predicts, with no free parameters, the dynamics of pair-rule expression patterns at different developmental time points and in various mutant backgrounds. Precise cellular identities are thus available at the earliest stages of development, contrasting the prevailing view of positional information being slowly refined across successive layers of the patterning network. Our results suggest that developmental enhancers closely approximate a mathematically optimal decoding strategy.
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Affiliation(s)
- Mariela D Petkova
- Joseph Henry Laboratories of Physics and the Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, NJ 08544, USA; Program in Biophysics, Harvard University, Cambridge, MA 02138, USA
| | - Gašper Tkačik
- Institute of Science and Technology Austria, Am Campus 1, 3400 Klosterneuburg, Austria
| | - William Bialek
- Joseph Henry Laboratories of Physics and the Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, NJ 08544, USA
| | - Eric F Wieschaus
- Department of Molecular Biology and Howard Hughes Medical Institute, Princeton University, Princeton, NJ 08544, USA
| | - Thomas Gregor
- Joseph Henry Laboratories of Physics and the Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, NJ 08544, USA; Department of Developmental and Stem Cell Biology, UMR3738, Institut Pasteur, 75015 Paris, France.
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10
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Monti M, Lubensky DK, Ten Wolde PR. Optimal entrainment of circadian clocks in the presence of noise. Phys Rev E 2018; 97:032405. [PMID: 29776095 DOI: 10.1103/physreve.97.032405] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/07/2017] [Indexed: 01/17/2023]
Abstract
Circadian clocks are biochemical oscillators that allow organisms to estimate the time of the day. These oscillators are inherently noisy due to the discrete nature of the reactants and the stochastic character of their interactions. To keep these oscillators in sync with the daily day-night rhythm in the presence of noise, circadian clocks must be coupled to the dark-light cycle. In this paper, we study the entrainment of phase oscillators as a function of the intrinsic noise in the system. Using stochastic simulations, we compute the optimal coupling strength, intrinsic frequency, and shape of the phase-response curve, that maximize the mutual information between the phase of the clock and time. We show that the optimal coupling strength and intrinsic frequency increase with the noise, but that the shape of the phase-response curve varies nonmonotonically with the noise: in the low-noise regime, it features a dead zone that increases in width as the noise increases, while in the high-noise regime, the width decreases with the noise. These results arise from a tradeoff between maximizing stability-noise suppression-and maximizing linearity of the input-output, i.e., time-phase, relation. We also show that three analytic approximations-the linear-noise approximation, the phase-averaging method, and linear-response theory-accurately describe different regimes of the coupling strength and the noise.
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Affiliation(s)
- Michele Monti
- AMOLF, Science Park 104, 1098 XE Amsterdam, The Netherlands
| | - David K Lubensky
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109-1040, USA
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11
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Crisanti A, De Martino A, Fiorentino J. Statistics of optimal information flow in ensembles of regulatory motifs. Phys Rev E 2018; 97:022407. [PMID: 29548237 DOI: 10.1103/physreve.97.022407] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/19/2017] [Indexed: 11/07/2022]
Abstract
Genetic regulatory circuits universally cope with different sources of noise that limit their ability to coordinate input and output signals. In many cases, optimal regulatory performance can be thought to correspond to configurations of variables and parameters that maximize the mutual information between inputs and outputs. Since the mid-2000s, such optima have been well characterized in several biologically relevant cases. Here we use methods of statistical field theory to calculate the statistics of the maximal mutual information (the "capacity") achievable by tuning the input variable only in an ensemble of regulatory motifs, such that a single controller regulates N targets. Assuming (i) sufficiently large N, (ii) quenched random kinetic parameters, and (iii) small noise affecting the input-output channels, we can accurately reproduce numerical simulations both for the mean capacity and for the whole distribution. Our results provide insight into the inherent variability in effectiveness occurring in regulatory systems with heterogeneous kinetic parameters.
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Affiliation(s)
- Andrea Crisanti
- Dipartimento di Fisica, Sapienza Università di Roma, piazzale Aldo Moro 5, 00185 Rome, Italy.,Istituto dei Sistemi Complessi, Consiglio Nazionale delle Ricerche, P.le Aldo Moro 2, 00185 Rome, Italy
| | - Andrea De Martino
- Soft and Living Matter Lab, Institute of Nanotechnology (CNR-NANOTEC), Consiglio Nazionale delle Ricerche, piazzale Aldo Moro 2, 00185 Rome, Italy.,Italian Institute for Genomic Medicine,Via Nizza 52, 10126 Turin, Italy
| | - Jonathan Fiorentino
- Dipartimento di Fisica, Sapienza Università di Roma, piazzale Aldo Moro 5, 00185 Rome, Italy
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12
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Bialek W. Perspectives on theory at the interface of physics and biology. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2018; 81:012601. [PMID: 29214982 DOI: 10.1088/1361-6633/aa995b] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Theoretical physics is the search for simple and universal mathematical descriptions of the natural world. In contrast, much of modern biology is an exploration of the complexity and diversity of life. For many, this contrast is prima facie evidence that theory, in the sense that physicists use the word, is impossible in a biological context. For others, this contrast serves to highlight a grand challenge. I am an optimist, and believe (along with many colleagues) that the time is ripe for the emergence of a more unified theoretical physics of biological systems, building on successes in thinking about particular phenomena. In this essay I try to explain the reasons for my optimism, through a combination of historical and modern examples.
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Affiliation(s)
- William Bialek
- Joseph Henry Laboratories of Physics, and Lewis-Sigler Institute for Integrative Genomics, Princeton University, 08544, Princeton NJ, United States of America. Initiative for the Theoretical Sciences, The Graduate Center, City University of New York, 365 Fifth Ave, 10016, New York NY, United States of America
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13
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Goldt S, Seifert U. Stochastic Thermodynamics of Learning. PHYSICAL REVIEW LETTERS 2017; 118:010601. [PMID: 28106416 DOI: 10.1103/physrevlett.118.010601] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/11/2016] [Indexed: 06/06/2023]
Abstract
Virtually every organism gathers information about its noisy environment and builds models from those data, mostly using neural networks. Here, we use stochastic thermodynamics to analyze the learning of a classification rule by a neural network. We show that the information acquired by the network is bounded by the thermodynamic cost of learning and introduce a learning efficiency η≤1. We discuss the conditions for optimal learning and analyze Hebbian learning in the thermodynamic limit.
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Affiliation(s)
- Sebastian Goldt
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Udo Seifert
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
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14
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Hillenbrand P, Gerland U, Tkačik G. Beyond the French Flag Model: Exploiting Spatial and Gene Regulatory Interactions for Positional Information. PLoS One 2016; 11:e0163628. [PMID: 27676252 PMCID: PMC5038966 DOI: 10.1371/journal.pone.0163628] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/29/2016] [Accepted: 09/12/2016] [Indexed: 11/18/2022] Open
Abstract
A crucial step in the early development of multicellular organisms involves the establishment of spatial patterns of gene expression which later direct proliferating cells to take on different cell fates. These patterns enable the cells to infer their global position within a tissue or an organism by reading out local gene expression levels. The patterning system is thus said to encode positional information, a concept that was formalized recently in the framework of information theory. Here we introduce a toy model of patterning in one spatial dimension, which can be seen as an extension of Wolpert’s paradigmatic “French Flag” model, to patterning by several interacting, spatially coupled genes subject to intrinsic and extrinsic noise. Our model, a variant of an Ising spin system, allows us to systematically explore expression patterns that optimally encode positional information. We find that optimal patterning systems use positional cues, as in the French Flag model, together with gene-gene interactions to generate combinatorial codes for position which we call “Counter” patterns. Counter patterns can also be stabilized against noise and variations in system size or morphogen dosage by longer-range spatial interactions of the type invoked in the Turing model. The simple setup proposed here qualitatively captures many of the experimentally observed properties of biological patterning systems and allows them to be studied in a single, theoretically consistent framework.
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Affiliation(s)
- Patrick Hillenbrand
- Physics of Complex Biosystems, Physics Department,Technical University of Munich, James-Franck-Str. 1, D-85748 Garching, Germany
| | - Ulrich Gerland
- Physics of Complex Biosystems, Physics Department,Technical University of Munich, James-Franck-Str. 1, D-85748 Garching, Germany
| | - Gašper Tkačik
- Institute of Science and Technology Austria, Am Campus 1, A-3400 Klosterneuburg, Austria
- * E-mail:
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15
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16
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Smith T, Fancher S, Levchenko A, Nemenman I, Mugler A. Role of spatial averaging in multicellular gradient sensing. Phys Biol 2016; 13:035004. [DOI: 10.1088/1478-3975/13/3/035004] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/23/2023]
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17
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Sokolowski TR, Walczak AM, Bialek W, Tkačik G. Extending the dynamic range of transcription factor action by translational regulation. Phys Rev E 2016; 93:022404. [PMID: 26986359 PMCID: PMC5221721 DOI: 10.1103/physreve.93.022404] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2015] [Indexed: 11/07/2022]
Abstract
A crucial step in the regulation of gene expression is binding of transcription factor (TF) proteins to regulatory sites along the DNA. But transcription factors act at nanomolar concentrations, and noise due to random arrival of these molecules at their binding sites can severely limit the precision of regulation. Recent work on the optimization of information flow through regulatory networks indicates that the lower end of the dynamic range of concentrations is simply inaccessible, overwhelmed by the impact of this noise. Motivated by the behavior of homeodomain proteins, such as the maternal morphogen Bicoid in the fruit fly embryo, we suggest a scheme in which transcription factors also act as indirect translational regulators, binding to the mRNA of other regulatory proteins. Intuitively, each mRNA molecule acts as an independent sensor of the input concentration, and averaging over these multiple sensors reduces the noise. We analyze information flow through this scheme and identify conditions under which it outperforms direct transcriptional regulation. Our results suggest that the dual role of homeodomain proteins is not just a historical accident, but a solution to a crucial physics problem in the regulation of gene expression.
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Affiliation(s)
- Thomas R. Sokolowski
- Institute of Science and Technology Austria, Am Campus 1, A-3400
Klosterneuburg, Austria
| | - Aleksandra M. Walczak
- CNRS-Laboratoire de Physique Théorique de
l’École Normale Supérieure, 24 rue Lhomond, F-75005 Paris,
France
| | - William Bialek
- Joseph Henry Laboratories of Physics, Lewis-Sigler Institute for
Integrative Genomics, Princeton University Princeton, New Jersey 08544, USA
| | - Gašper Tkačik
- Institute of Science and Technology Austria, Am Campus 1, A-3400
Klosterneuburg, Austria
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18
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Limits to the precision of gradient sensing with spatial communication and temporal integration. Proc Natl Acad Sci U S A 2016; 113:E689-95. [PMID: 26792517 DOI: 10.1073/pnas.1509597112] [Citation(s) in RCA: 53] [Impact Index Per Article: 6.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023] Open
Abstract
Gradient sensing requires at least two measurements at different points in space. These measurements must then be communicated to a common location to be compared, which is unavoidably noisy. Although much is known about the limits of measurement precision by cells, the limits placed by the communication are not understood. Motivated by recent experiments, we derive the fundamental limits to the precision of gradient sensing in a multicellular system, accounting for communication and temporal integration. The gradient is estimated by comparing a "local" and a "global" molecular reporter of the external concentration, where the global reporter is exchanged between neighboring cells. Using the fluctuation-dissipation framework, we find, in contrast to the case when communication is ignored, that precision saturates with the number of cells independently of the measurement time duration, because communication establishes a maximum length scale over which sensory information can be reliably conveyed. Surprisingly, we also find that precision is improved if the local reporter is exchanged between cells as well, albeit more slowly than the global reporter. The reason is that whereas exchange of the local reporter weakens the comparison, it decreases the measurement noise. We term such a model "regional excitation-global inhibition." Our results demonstrate that fundamental sensing limits are necessarily sharpened when the need to communicate information is taken into account.
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19
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Cell-cell communication enhances the capacity of cell ensembles to sense shallow gradients during morphogenesis. Proc Natl Acad Sci U S A 2016; 113:E679-88. [PMID: 26792522 DOI: 10.1073/pnas.1516503113] [Citation(s) in RCA: 100] [Impact Index Per Article: 12.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/17/2023] Open
Abstract
Collective cell responses to exogenous cues depend on cell-cell interactions. In principle, these can result in enhanced sensitivity to weak and noisy stimuli. However, this has not yet been shown experimentally, and little is known about how multicellular signal processing modulates single-cell sensitivity to extracellular signaling inputs, including those guiding complex changes in the tissue form and function. Here we explored whether cell-cell communication can enhance the ability of cell ensembles to sense and respond to weak gradients of chemotactic cues. Using a combination of experiments with mammary epithelial cells and mathematical modeling, we find that multicellular sensing enables detection of and response to shallow epidermal growth factor (EGF) gradients that are undetectable by single cells. However, the advantage of this type of gradient sensing is limited by the noisiness of the signaling relay, necessary to integrate spatially distributed ligand concentration information. We calculate the fundamental sensory limits imposed by this communication noise and combine them with the experimental data to estimate the effective size of multicellular sensory groups involved in gradient sensing. Functional experiments strongly implicated intercellular communication through gap junctions and calcium release from intracellular stores as mediators of collective gradient sensing. The resulting integrative analysis provides a framework for understanding the advantages and limitations of sensory information processing by relays of chemically coupled cells.
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Tikhonov M, Little SC, Gregor T. Only accessible information is useful: insights from gradient-mediated patterning. ROYAL SOCIETY OPEN SCIENCE 2015; 2:150486. [PMID: 26716005 PMCID: PMC4680620 DOI: 10.1098/rsos.150486] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/14/2015] [Accepted: 10/29/2015] [Indexed: 06/01/2023]
Abstract
Information theory is gaining popularity as a tool to characterize performance of biological systems. However, information is commonly quantified without reference to whether or how a system could extract and use it; as a result, information-theoretic quantities are easily misinterpreted. Here, we take the example of pattern-forming developmental systems which are commonly structured as cascades of sequential gene expression steps. Such a multi-tiered structure appears to constitute sub-optimal use of the positional information provided by the input morphogen because noise is added at each tier. However, one must distinguish between the total information in a morphogen and information that can be usefully extracted and interpreted by downstream elements. We demonstrate that quantifying the information that is accessible to the system naturally explains the prevalence of multi-tiered network architectures as a consequence of the noise inherent to the control of gene expression. We support our argument with empirical observations from patterning along the major body axis of the fruit fly embryo. We use this example to highlight the limitations of the standard information-theoretic characterization of biological signalling, which are frequently de-emphasized, and illustrate how they can be resolved.
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Affiliation(s)
- Mikhail Tikhonov
- Joseph Henry Laboratories of Physics, Princeton University, Princeton, NJ 08544, USA
- Harvard Center of Mathematical Sciences and Applications, Harvard University, Cambridge, MA 02138, USA
- Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA
- Kavli Institute for Bionano Science and Technology, Harvard University, Cambridge, MA 02138, USA
| | - Shawn C. Little
- Joseph Henry Laboratories of Physics, Princeton University, Princeton, NJ 08544, USA
- Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, NJ 08544, USA
| | - Thomas Gregor
- Joseph Henry Laboratories of Physics, Princeton University, Princeton, NJ 08544, USA
- Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, NJ 08544, USA
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