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Ho EK, Oatman HR, McFann SE, Yang L, Johnson HE, Shvartsman SY, Toettcher JE. Dynamics of an incoherent feedforward loop drive ERK-dependent pattern formation in the early Drosophila embryo. Development 2023; 150:dev201818. [PMID: 37602510 PMCID: PMC10482391 DOI: 10.1242/dev.201818] [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: 03/29/2023] [Accepted: 08/11/2023] [Indexed: 08/22/2023]
Abstract
Positional information in development often manifests as stripes of gene expression, but how stripes form remains incompletely understood. Here, we use optogenetics and live-cell biosensors to investigate the posterior brachyenteron (byn) stripe in early Drosophila embryos. This stripe depends on interpretation of an upstream ERK activity gradient and the expression of two target genes, tailless (tll) and huckebein (hkb), that exert antagonistic control over byn. We find that high or low doses of ERK signaling produce transient or sustained byn expression, respectively. Although tll transcription is always rapidly induced, hkb converts graded ERK inputs into a variable time delay. Nuclei thus interpret ERK amplitude through the relative timing of tll and hkb transcription. Antagonistic regulatory paths acting on different timescales are hallmarks of an incoherent feedforward loop, which is sufficient to explain byn dynamics and adds temporal complexity to the steady-state model of byn stripe formation. We further show that 'blurring' of an all-or-none stimulus through intracellular diffusion non-locally produces a byn stripe. Overall, we provide a blueprint for using optogenetics to dissect developmental signal interpretation in space and time.
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Affiliation(s)
- Emily K. Ho
- Department of Molecular Biology, Princeton University, Princeton, NJ 08544, USA
| | - Harrison R. Oatman
- Program in Quantitative and Computational Biology, Princeton University, Princeton, NJ 08544, USA
| | - Sarah E. McFann
- Department of Chemical & Biological Engineering, Princeton University, Princeton, NJ 08544, USA
| | - Liu Yang
- Lewis Sigler Institute for Integrative Genomics, Princeton University, Princeton, NJ 08544, USA
| | - Heath E. Johnson
- Department of Molecular Biology, Princeton University, Princeton, NJ 08544, USA
| | - Stanislav Y. Shvartsman
- Department of Molecular Biology, Princeton University, Princeton, NJ 08544, USA
- Lewis Sigler Institute for Integrative Genomics, Princeton University, Princeton, NJ 08544, USA
- Center for Computational Biology, Flatiron Institute - Simons Foundation, New York, NY 10010, USA
| | - Jared E. Toettcher
- Department of Molecular Biology, Princeton University, Princeton, NJ 08544, USA
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2
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Lee K, O’Neill KM, Ku J, Shvartsman SY, Kim Y. Patterning potential of the terminal system in the Drosophila embryo. KOREAN J CHEM ENG 2023. [DOI: 10.1007/s11814-022-1298-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/05/2023]
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3
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Marmion RA, Yang L, Goyal Y, Jindal GA, Wetzel JL, Singh M, Schüpbach T, Shvartsman SY. Molecular mechanisms underlying cellular effects of human MEK1 mutations. Mol Biol Cell 2021; 32:974-983. [PMID: 33476180 PMCID: PMC8108529 DOI: 10.1091/mbc.e20-10-0625] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022] Open
Abstract
Terminal regions of Drosophila embryos are patterned by signaling through ERK, which is genetically deregulated in multiple human diseases. Quantitative studies of terminal patterning have been recently used to investigate gain-of-function variants of human MEK1, encoding the MEK kinase that directly activates ERK by dual phosphorylation. Unexpectedly, several mutations reduced ERK activation by extracellular signals, possibly through a negative feedback triggered by signal-independent activity of the mutant variants. Here we present experimental evidence supporting this model. Using a MEK variant that combines a mutation within the negative regulatory region with alanine substitutions in the activation loop, we prove that pathogenic variants indeed acquire signal-independent kinase activity. We also demonstrate that signal-dependent activation of these variants is independent of kinase suppressor of Ras, a conserved adaptor that is indispensable for activation of normal MEK. Finally, we show that attenuation of ERK activation by extracellular signals stems from transcriptional induction of Mkp3, a dual specificity phosphatase that deactivates ERK by dephosphorylation. These findings in the Drosophila embryo highlight its power for investigating diverse effects of human disease mutations.
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Affiliation(s)
- Robert A Marmion
- Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, NJ 08544
| | - Liu Yang
- Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, NJ 08544
| | - Yogesh Goyal
- Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, NJ 08544.,Department of Chemical and Biological Engineering, Princeton University, Princeton, NJ 08544.,Department of Bioengineering, University of Pennsylvania, Philadelphia, PA 19104
| | - Granton A Jindal
- Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, NJ 08544.,Department of Chemical and Biological Engineering, Princeton University, Princeton, NJ 08544.,Department of Medicine, University of California San Diego, La Jolla, CA 92093
| | - Joshua L Wetzel
- Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, NJ 08544.,Department of Computer Science, Princeton University, Princeton, NJ 08540
| | - Mona Singh
- Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, NJ 08544.,Department of Computer Science, Princeton University, Princeton, NJ 08540
| | - Trudi Schüpbach
- Department of Molecular Biology, Princeton University, Princeton, NJ 08544
| | - Stanislav Y Shvartsman
- Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, NJ 08544.,Department of Chemical and Biological Engineering, Princeton University, Princeton, NJ 08544.,Department of Molecular Biology, Princeton University, Princeton, NJ 08544.,Flatiron Institute, Simons Foundation, New York, NY 10010
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4
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Abstract
Terminal regions of the early Drosophila embryo are patterned by the highly conserved ERK cascade, giving rise to the nonsegmented terminal structures of the future larva. In less than an hour, this signaling event establishes several gene expression boundaries and sets in motion a sequence of elaborate morphogenetic events. Genetic studies of terminal patterning discovered signaling components and transcription factors that are involved in numerous developmental contexts and deregulated in human diseases. This review summarizes current understanding of signaling and morphogenesis during terminal patterning and discusses several open questions that can now be rigorously investigated using live imaging, omics, and optogenetic approaches. The anatomical simplicity of the terminal patterning system and its amenability to a broad range of increasingly sophisticated genetic perturbations will continue to make it a premier quantitative model for studying multiple aspects of tissue patterning by dynamically controlled cell signaling pathways.
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5
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Metabolic Regulation of Developmental Cell Cycles and Zygotic Transcription. Curr Biol 2019; 29:1193-1198.e5. [PMID: 30880009 DOI: 10.1016/j.cub.2019.02.028] [Citation(s) in RCA: 21] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/30/2018] [Revised: 01/15/2019] [Accepted: 02/08/2019] [Indexed: 12/29/2022]
Abstract
The thirteen nuclear cleavages that give rise to the Drosophila blastoderm are some of the fastest known cell cycles [1]. Surprisingly, the fertilized egg is provided with at most one-third of the dNTPs needed to complete the thirteen rounds of DNA replication [2]. The rest must be synthesized by the embryo, concurrent with cleavage divisions. What is the reason for the limited supply of DNA building blocks? We propose that frugal control of dNTP synthesis contributes to the well-characterized deceleration of the cleavage cycles and is needed for robust accumulation of zygotic gene products. In support of this model, we demonstrate that when the levels of dNTPs are abnormally high, nuclear cleavages fail to sufficiently decelerate, the levels of zygotic transcription are dramatically reduced, and the embryo catastrophically fails early in gastrulation. Our work reveals a direct connection between metabolism, the cell cycle, and zygotic transcription.
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6
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Goyal Y, Schüpbach T, Shvartsman SY. A quantitative model of developmental RTK signaling. Dev Biol 2018; 442:80-86. [PMID: 30026122 DOI: 10.1016/j.ydbio.2018.07.012] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/19/2018] [Revised: 06/22/2018] [Accepted: 07/13/2018] [Indexed: 01/06/2023]
Abstract
Receptor tyrosine kinases (RTKs) control a wide range of developmental processes, from the first stages of embryogenesis to postnatal growth and neurocognitive development in the adult. A significant share of our knowledge about RTKs comes from genetic screens in model organisms, which provided numerous examples demonstrating how specific cell fates and morphologies are abolished when RTK activation is either abrogated or significantly reduced. Aberrant activation of such pathways has also been recognized in many forms of cancer. More recently, studies of human developmental syndromes established that excessive activation of RTKs and their downstream signaling effectors, most notably the Ras signaling pathway, can also lead to structural and functional defects. Given that both insufficient and excessive pathway activation can lead to abnormalities, mechanistic analysis of developmental RTK signaling must address quantitative questions about its regulation and function. Patterning events controlled by the RTK Torso in the early Drosophila embryo are well-suited for this purpose. This mini review summarizes current state of knowledge about Torso-dependent Ras activation and discusses its potential to serve as a quantitative model for studying the general principles of Ras signaling in development and disease.
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Affiliation(s)
- Yogesh Goyal
- Department of Chemical and Biological Engineering, Princeton University, Princeton, NJ 08544, United States; The Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, NJ 08544, United States
| | - Trudi Schüpbach
- Department of Molecular Biology, Princeton University, Princeton, NJ 08544, United States
| | - Stanislav Y Shvartsman
- Department of Chemical and Biological Engineering, Princeton University, Princeton, NJ 08544, United States; The Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, NJ 08544, United States; Department of Molecular Biology, Princeton University, Princeton, NJ 08544, United States.
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7
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Broadly expressed repressors integrate patterning across orthogonal axes in embryos. Proc Natl Acad Sci U S A 2017; 114:8295-8300. [PMID: 28720706 DOI: 10.1073/pnas.1703001114] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
The role of spatially localized repressors in supporting embryonic patterning is well appreciated, but, alternatively, the role ubiquitously expressed repressors play in this process is not well understood. We investigated the function of two broadly expressed repressors, Runt (Run) and Suppressor of Hairless [Su(H)], in patterning the Drosophila embryo. Previous studies have shown that Run and Su(H) regulate gene expression along anterior-posterior (AP) or dorsal-ventral (DV) axes, respectively, by spatially limiting activator action, but here we characterize a different role. Our data show that broadly expressed repressors silence particular enhancers within cis-regulatory systems, blocking their expression throughout the embryo fully but transiently, and, in this manner, regulate spatiotemporal outputs along both axes. Our results suggest that Run and Su(H) regulate the temporal action of enhancers and are not dedicated regulators of one axis but, instead, act coordinately to pattern both axes, AP and DV.
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LeBlanc VG, Firme M, Song J, Chan SY, Lee MH, Yip S, Chittaranjan S, Marra MA. Comparative transcriptome analysis of isogenic cell line models and primary cancers links capicua (CIC) loss to activation of the MAPK signalling cascade. J Pathol 2017; 242:206-220. [PMID: 28295365 PMCID: PMC5485162 DOI: 10.1002/path.4894] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/16/2017] [Revised: 02/27/2017] [Accepted: 03/09/2017] [Indexed: 01/30/2023]
Abstract
CIC encodes a transcriptional repressor, capicua (CIC), whose disrupted activity appears to be involved in several cancer types, including type I low‐grade gliomas (LGGs) and stomach adenocarcinomas (STADs). To explore human CIC's transcriptional network in an isogenic background, we developed novel isogenic CIC knockout cell lines as model systems, and used these in transcriptome analyses to study the consequences of CIC loss. We also compared our results with analyses of transcriptome data from TCGA for type I LGGs and STADs. We identified 39 candidate targets of CIC transcriptional regulation, and confirmed seven of these as direct targets. We showed that, although many CIC targets appear to be context‐specific, the effects of CIC loss converge on the dysregulation of similar biological processes in different cancer types. For example, we found that CIC deficiency was associated with disruptions in the expression of genes involved in cell–cell adhesion, and in the development of several cell and tissue types. We also showed that loss of CIC leads to overexpression of downstream members of the mitogen‐activated protein kinase (MAPK) signalling cascade, indicating that CIC deficiency may present a novel mechanism for activation of this oncogenic pathway. © 2017 The Authors. Journal of Pathology published by John Wiley & Sons Ltd on behalf of Pathological Society of Great Britain and Ireland.
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Affiliation(s)
- Veronique G LeBlanc
- Canada's Michael Smith Genome Sciences Centre, BC Cancer Agency, Vancouver, BC, Canada.,Genome Science and Technology Program, University of British Columbia, Vancouver, BC, Canada
| | - Marlo Firme
- Canada's Michael Smith Genome Sciences Centre, BC Cancer Agency, Vancouver, BC, Canada
| | - Jungeun Song
- Canada's Michael Smith Genome Sciences Centre, BC Cancer Agency, Vancouver, BC, Canada
| | - Susanna Y Chan
- Canada's Michael Smith Genome Sciences Centre, BC Cancer Agency, Vancouver, BC, Canada
| | - Min Hye Lee
- Canada's Michael Smith Genome Sciences Centre, BC Cancer Agency, Vancouver, BC, Canada
| | - Stephen Yip
- Department of Pathology and Laboratory Medicine, University of British Columbia, BC, Canada
| | - Suganthi Chittaranjan
- Canada's Michael Smith Genome Sciences Centre, BC Cancer Agency, Vancouver, BC, Canada
| | - Marco A Marra
- Canada's Michael Smith Genome Sciences Centre, BC Cancer Agency, Vancouver, BC, Canada.,Department of Medical Genetics, University of British Columbia, Vancouver, BC, Canada
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9
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Goyal Y, Jindal GA, Pelliccia JL, Yamaya K, Yeung E, Futran AS, Burdine RD, Schüpbach T, Shvartsman SY. Divergent effects of intrinsically active MEK variants on developmental Ras signaling. Nat Genet 2017; 49:465-469. [PMID: 28166211 PMCID: PMC5621734 DOI: 10.1038/ng.3780] [Citation(s) in RCA: 43] [Impact Index Per Article: 6.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/03/2016] [Accepted: 12/30/2016] [Indexed: 12/16/2022]
Abstract
Germline mutations in Ras pathway components are associated with a large class of human developmental abnormalities, known as RASopathies, that are characterized by a range of structural and functional phenotypes, including cardiac defects and neurocognitive delays. Although it is generally believed that RASopathies are caused by altered levels of pathway activation, the signaling changes in developing tissues remain largely unknown. We used assays with spatiotemporal resolution in Drosophila melanogaster (fruit fly) and Danio rerio (zebrafish) to quantify signaling changes caused by mutations in MAP2K1 (encoding MEK), a core component of the Ras pathway that is mutated in both RASopathies and cancers in humans. Surprisingly, we discovered that intrinsically active MEK variants can both increase and reduce the levels of pathway activation in vivo. The sign of the effect depends on cellular context, implying that some of the emerging phenotypes in RASopathies may be caused by increased, as well as attenuated, levels of Ras signaling.
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Affiliation(s)
- Yogesh Goyal
- Department of Chemical and Biological Engineering, Princeton University, Princeton, NJ 08544
- The Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, NJ 08544
| | - Granton A. Jindal
- Department of Chemical and Biological Engineering, Princeton University, Princeton, NJ 08544
- The Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, NJ 08544
- Department of Molecular Biology, Princeton University, Princeton, NJ 08544
| | - José L. Pelliccia
- Department of Molecular Biology, Princeton University, Princeton, NJ 08544
| | - Kei Yamaya
- The Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, NJ 08544
- Department of Molecular Biology, Princeton University, Princeton, NJ 08544
| | - Eyan Yeung
- The Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, NJ 08544
- Department of Molecular Biology, Princeton University, Princeton, NJ 08544
| | - Alan S. Futran
- Department of Chemical and Biological Engineering, Princeton University, Princeton, NJ 08544
- The Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, NJ 08544
| | - Rebecca D. Burdine
- Department of Molecular Biology, Princeton University, Princeton, NJ 08544
| | - Trudi Schüpbach
- Department of Molecular Biology, Princeton University, Princeton, NJ 08544
| | - Stanislav Y. Shvartsman
- Department of Chemical and Biological Engineering, Princeton University, Princeton, NJ 08544
- The Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, NJ 08544
- Department of Molecular Biology, Princeton University, Princeton, NJ 08544
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10
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Temporal and spatial dynamics of scaling-specific features of a gene regulatory network in Drosophila. Nat Commun 2015; 6:10031. [PMID: 26644070 PMCID: PMC4686680 DOI: 10.1038/ncomms10031] [Citation(s) in RCA: 38] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/13/2015] [Accepted: 10/28/2015] [Indexed: 01/19/2023] Open
Abstract
A widely appreciated aspect of developmental robustness is pattern formation in proportion to size. But how such scaling features emerge dynamically remains poorly understood. Here we generate a data set of the expression profiles of six gap genes in Drosophila melanogaster embryos that differ significantly in size. Expression patterns exhibit size-dependent dynamics both spatially and temporally. We uncover a dynamic emergence of under-scaling in the posterior, accompanied by reduced expression levels of gap genes near the middle of large embryos. Simulation results show that a size-dependent Bicoid gradient input can lead to reduced Krüppel expression that can have long-range and dynamic effects on gap gene expression in the posterior. Thus, for emergence of scaled patterns, the entire embryo may be viewed as a single unified dynamic system where maternally derived size-dependent information interpreted locally can be propagated in space and time as governed by the dynamics of a gene regulatory network. How pattern formation is regulated relative to the size of an organism is unclear. Here, Wu et al. take data from gap gene expression in flies of different sizes together with simulations, identifying how scaling emerges dynamically and that local patterning influences global gene regulatory networks.
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11
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Mapping the binding interface of ERK and transcriptional repressor Capicua using photocrosslinking. Proc Natl Acad Sci U S A 2015; 112:8590-5. [PMID: 26124095 DOI: 10.1073/pnas.1501373112] [Citation(s) in RCA: 35] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Extracellular signal-regulated kinase (ERK) coordinates cellular responses to a range of stimuli by phosphorylating its numerous substrates. One of these substrates, Capicua (Cic), is a transcriptional repressor that was first identified in Drosophila and has been implicated in a number of human diseases. Here we use a chemical biology approach to map the binding interface of ERK and Cic. The noncanonical amino acid p-azidophenylalanine (AzF) was introduced into the ERK-binding region of Drosophila Cic, and photocrosslinking and tandem mass spectrometry were used to pinpoint its binding site on ERK. We also identified the ERK-binding region of human Cic and showed that it binds to the same site on ERK despite lacking conservation with the Drosophila Cic binding region. Finally, we mapped the amino acids involved in human Cic binding to ERK using AzF-labeled ERK. These results reveal the molecular details of the ERK-Cic interaction and demonstrate that the photocrosslinking approach is complementary to existing methods for mapping kinase-substrate binding interfaces.
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12
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Abstract
Spatial patterns in the early fruit fly embryo emerge from a network of interactions among transcription factors, the gap genes, driven by maternal inputs. Such networks can exhibit many qualitatively different behaviors, separated by critical surfaces. At criticality, we should observe strong correlations in the fluctuations of different genes around their mean expression levels, a slowing of the dynamics along some but not all directions in the space of possible expression levels, correlations of expression fluctuations over long distances in the embryo, and departures from a Gaussian distribution of these fluctuations. Analysis of recent experiments on the gap gene network shows that all these signatures are observed, and that the different signatures are related in ways predicted by theory. Although there might be other explanations for these individual phenomena, the confluence of evidence suggests that this genetic network is tuned to criticality.
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Affiliation(s)
- Dmitry Krotov
- Joseph Henry Laboratories of Physics, Lewis–Sigler Institute for Integrative Genomics, and
| | - Julien O. Dubuis
- Joseph Henry Laboratories of Physics, Lewis–Sigler Institute for Integrative Genomics, and
- Howard Hughes Medical Institute, Princeton University, Princeton, NJ 08544
| | - Thomas Gregor
- Joseph Henry Laboratories of Physics, Lewis–Sigler Institute for Integrative Genomics, and
| | - William Bialek
- Joseph Henry Laboratories of Physics, Lewis–Sigler Institute for Integrative Genomics, and
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13
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Albert R, Collins JJ, Glass L. Introduction to focus issue: quantitative approaches to genetic networks. CHAOS (WOODBURY, N.Y.) 2013; 23:025001. [PMID: 23822498 DOI: 10.1063/1.4810923] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
All cells of living organisms contain similar genetic instructions encoded in the organism's DNA. In any particular cell, the control of the expression of each different gene is regulated, in part, by binding of molecular complexes to specific regions of the DNA. The molecular complexes are composed of protein molecules, called transcription factors, combined with various other molecules such as hormones and drugs. Since transcription factors are coded by genes, cellular function is partially determined by genetic networks. Recent research is making large strides to understand both the structure and the function of these networks. Further, the emerging discipline of synthetic biology is engineering novel gene circuits with specific dynamic properties to advance both basic science and potential practical applications. Although there is not yet a universally accepted mathematical framework for studying the properties of genetic networks, the strong analogies between the activation and inhibition of gene expression and electric circuits suggest frameworks based on logical switching circuits. This focus issue provides a selection of papers reflecting current research directions in the quantitative analysis of genetic networks. The work extends from molecular models for the binding of proteins, to realistic detailed models of cellular metabolism. Between these extremes are simplified models in which genetic dynamics are modeled using classical methods of systems engineering, Boolean switching networks, differential equations that are continuous analogues of Boolean switching networks, and differential equations in which control is based on power law functions. The mathematical techniques are applied to study: (i) naturally occurring gene networks in living organisms including: cyanobacteria, Mycoplasma genitalium, fruit flies, immune cells in mammals; (ii) synthetic gene circuits in Escherichia coli and yeast; and (iii) electronic circuits modeling genetic networks using field-programmable gate arrays. Mathematical analyses will be essential for understanding naturally occurring genetic networks in diverse organisms and for providing a foundation for the improved development of synthetic genetic networks.
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Affiliation(s)
- Réka Albert
- Department of Physics, Penn State University, University Park, Pennsylvania 16802, USA
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