1
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Li Y, Deng D, Höfer CT, Kim J, Do Heo W, Xu Q, Liu X, Zi Z. Liebig's law of the minimum in the TGF-β/SMAD pathway. PLoS Comput Biol 2024; 20:e1012072. [PMID: 38753874 DOI: 10.1371/journal.pcbi.1012072] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/14/2024] [Accepted: 04/11/2024] [Indexed: 05/18/2024] Open
Abstract
Cells use signaling pathways to sense and respond to their environments. The transforming growth factor-β (TGF-β) pathway produces context-specific responses. Here, we combined modeling and experimental analysis to study the dependence of the output of the TGF-β pathway on the abundance of signaling molecules in the pathway. We showed that the TGF-β pathway processes the variation of TGF-β receptor abundance using Liebig's law of the minimum, meaning that the output-modifying factor is the signaling protein that is most limited, to determine signaling responses across cell types and in single cells. We found that the abundance of either the type I (TGFBR1) or type II (TGFBR2) TGF-β receptor determined the responses of cancer cell lines, such that the receptor with relatively low abundance dictates the response. Furthermore, nuclear SMAD2 signaling correlated with the abundance of TGF-β receptor in single cells depending on the relative expression levels of TGFBR1 and TGFBR2. A similar control principle could govern the heterogeneity of signaling responses in other signaling pathways.
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Affiliation(s)
- Yuchao Li
- Max Planck Institute for Molecular Genetics, Otto Warburg Laboratory, Berlin, Germany
| | - Difan Deng
- German Federal Institute for Risk Assessment, Department of Experimental Toxicology and ZEBET, Berlin, Germany
| | - Chris Tina Höfer
- German Federal Institute for Risk Assessment, Department of Experimental Toxicology and ZEBET, Berlin, Germany
| | - Jihye Kim
- Department of Biological Sciences, KAIST Institute for the BioCentury, Korea Advanced Institute of Science and Technology (KAIST), Daejeon, Republic of Korea
| | - Won Do Heo
- Department of Biological Sciences, KAIST Institute for the BioCentury, Korea Advanced Institute of Science and Technology (KAIST), Daejeon, Republic of Korea
| | - Quanbin Xu
- Department of Biochemistry, University of Colorado Boulder, Boulder, Colorado, United States of America
| | - Xuedong Liu
- Department of Biochemistry, University of Colorado Boulder, Boulder, Colorado, United States of America
| | - Zhike Zi
- Max Planck Institute for Molecular Genetics, Otto Warburg Laboratory, Berlin, Germany
- German Federal Institute for Risk Assessment, Department of Experimental Toxicology and ZEBET, Berlin, Germany
- Key Laboratory of Quantitative Synthetic Biology, Shenzhen Institute of Synthetic Biology, Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences, Shenzhen, China
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2
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Ram A, Murphy D, DeCuzzi N, Patankar M, Hu J, Pargett M, Albeck JG. A guide to ERK dynamics, part 1: mechanisms and models. Biochem J 2023; 480:1887-1907. [PMID: 38038974 PMCID: PMC10754288 DOI: 10.1042/bcj20230276] [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: 07/09/2023] [Revised: 11/02/2023] [Accepted: 11/06/2023] [Indexed: 12/02/2023]
Abstract
Extracellular signal-regulated kinase (ERK) has long been studied as a key driver of both essential cellular processes and disease. A persistent question has been how this single pathway is able to direct multiple cell behaviors, including growth, proliferation, and death. Modern biosensor studies have revealed that the temporal pattern of ERK activity is highly variable and heterogeneous, and critically, that these dynamic differences modulate cell fate. This two-part review discusses the current understanding of dynamic activity in the ERK pathway, how it regulates cellular decisions, and how these cell fates lead to tissue regulation and pathology. In part 1, we cover the optogenetic and live-cell imaging technologies that first revealed the dynamic nature of ERK, as well as current challenges in biosensor data analysis. We also discuss advances in mathematical models for the mechanisms of ERK dynamics, including receptor-level regulation, negative feedback, cooperativity, and paracrine signaling. While hurdles still remain, it is clear that higher temporal and spatial resolution provide mechanistic insights into pathway circuitry. Exciting new algorithms and advanced computational tools enable quantitative measurements of single-cell ERK activation, which in turn inform better models of pathway behavior. However, the fact that current models still cannot fully recapitulate the diversity of ERK responses calls for a deeper understanding of network structure and signal transduction in general.
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Affiliation(s)
- Abhineet Ram
- Department of Molecular and Cellular Biology, University of California, Davis, U.S.A
| | - Devan Murphy
- Department of Molecular and Cellular Biology, University of California, Davis, U.S.A
| | - Nicholaus DeCuzzi
- Department of Molecular and Cellular Biology, University of California, Davis, U.S.A
| | - Madhura Patankar
- Department of Molecular and Cellular Biology, University of California, Davis, U.S.A
| | - Jason Hu
- Department of Molecular and Cellular Biology, University of California, Davis, U.S.A
| | - Michael Pargett
- Department of Molecular and Cellular Biology, University of California, Davis, U.S.A
| | - John G. Albeck
- Department of Molecular and Cellular Biology, University of California, Davis, U.S.A
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3
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Roesch E, Greener JG, MacLean AL, Nassar H, Rackauckas C, Holy TE, Stumpf MPH. Julia for biologists. Nat Methods 2023; 20:655-664. [PMID: 37024649 PMCID: PMC10216852 DOI: 10.1038/s41592-023-01832-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/21/2021] [Accepted: 02/27/2023] [Indexed: 04/08/2023]
Abstract
Major computational challenges exist in relation to the collection, curation, processing and analysis of large genomic and imaging datasets, as well as the simulation of larger and more realistic models in systems biology. Here we discuss how a relative newcomer among programming languages-Julia-is poised to meet the current and emerging demands in the computational biosciences and beyond. Speed, flexibility, a thriving package ecosystem and readability are major factors that make high-performance computing and data analysis available to an unprecedented degree. We highlight how Julia's design is already enabling new ways of analyzing biological data and systems, and we provide a list of resources that can facilitate the transition into Julian computing.
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Affiliation(s)
- Elisabeth Roesch
- School of Mathematics and Statistics, University of Melbourne, Melbourne, Victoria, Australia
- Melbourne Integrative Genomics, University of Melbourne, Melbourne, Victoria, Australia
- JuliaHub, Somerville, MA, USA
| | - Joe G Greener
- Medical Research Council Laboratory of Molecular Biology, Cambridge, UK
| | - Adam L MacLean
- Department of Quantitative and Computational Biology, University of Southern California, Los Angeles, CA, USA
| | | | - Christopher Rackauckas
- JuliaHub, Somerville, MA, USA
- Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, USA
- Pumas-AI, Centreville, VA, USA
| | - Timothy E Holy
- Departments of Neuroscience and Biomedical Engineering, Washington University in St. Louis, St. Louis, MO, USA
| | - Michael P H Stumpf
- School of Mathematics and Statistics, University of Melbourne, Melbourne, Victoria, Australia.
- Melbourne Integrative Genomics, University of Melbourne, Melbourne, Victoria, Australia.
- School of BioSciences, The University of Melbourne, Melbourne, Victoria, Australia.
- ARC Centre of Excellence for the Mathematical Analysis of Cellular Systems, Melbourne, Victoria, Australia.
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4
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Zheng X, Chen L, Chen T, Cao M, Zhang B, Yuan C, Zhao Z, Li C, Zhou X. The Mechanisms of BDNF Promoting the Proliferation of Porcine Follicular Granulosa Cells: Role of miR-127 and Involvement of the MAPK-ERK1/2 Pathway. Animals (Basel) 2023; 13:ani13061115. [PMID: 36978655 PMCID: PMC10044701 DOI: 10.3390/ani13061115] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/28/2023] [Revised: 03/16/2023] [Accepted: 03/20/2023] [Indexed: 03/30/2023] Open
Abstract
As a member of the neurotrophic family, brain-derived neurotrophic factor (BDNF) provides a key link in the physiological process of mammalian ovarian follicle development, in addition to its functions in the nervous system. The emphasis of this study lay in the impact of BDNF on the proliferation of porcine follicular granulosa cells (GCs) in vitro. BDNF and tyrosine kinase B (TrkB, receptor of BDNF) were detected in porcine follicular GCs. Additionally, cell viability significantly increased during the culture of porcine GCs with BDNF (100 ng/mL) in vitro. However, BDNF knockdown in GCs decreased cell viability and S-phase cells proportion-and BDNF simultaneously regulated the expression of genes linked with cell proliferation (CCND1, p21 and Bcl2) and apoptosis (Bax). Then, the results of the receptor blocking experiment showed that BDNF promoted GC proliferation via TrkB. The high-throughput sequencing showed that BDNF also regulated the expression profiles of miRNAs in GCs. The differential expression profiles were obtained by miRNA sequencing after BDNF (100 ng/mL) treatment with GCs. The sequencing results showed that, after BDNF treatment, 72 significant differentially-expressed miRNAs were detected-5 of which were related to cell process and proliferation signaling pathways confirmed by RT-PCR. Furthermore, studies showed that BDNF promoted GCs' proliferation by increasing the expression of CCND1, downregulating miR-127 and activating the ERK1/2 signal pathway. Moreover, BDNF indirectly activated the ERK1/2 signal pathway by downregulating miR-127. In conclusion, BDNF promoted porcine GC proliferation by increasing CCND1 expression, downregulating miR-127 and stimulating the MAPK-ERK1/2 signaling cascade.
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Affiliation(s)
- Xue Zheng
- Laboratory for Regulation of Reproduction, College of Animal Sciences, Jilin University, Changchun 130062, China
- College of Biological and Pharmaceutical Engineering, Jilin Agricultural Science and Technology University, Jilin 132101, China
| | - Lu Chen
- Laboratory for Regulation of Reproduction, College of Animal Sciences, Jilin University, Changchun 130062, China
| | - Tong Chen
- Laboratory for Regulation of Reproduction, College of Animal Sciences, Jilin University, Changchun 130062, China
| | - Maosheng Cao
- Laboratory for Regulation of Reproduction, College of Animal Sciences, Jilin University, Changchun 130062, China
| | - Boqi Zhang
- Laboratory for Regulation of Reproduction, College of Animal Sciences, Jilin University, Changchun 130062, China
| | - Chenfeng Yuan
- Laboratory for Regulation of Reproduction, College of Animal Sciences, Jilin University, Changchun 130062, China
| | - Zijiao Zhao
- Laboratory for Regulation of Reproduction, College of Animal Sciences, Jilin University, Changchun 130062, China
| | - Chunjin Li
- Laboratory for Regulation of Reproduction, College of Animal Sciences, Jilin University, Changchun 130062, China
| | - Xu Zhou
- Laboratory for Regulation of Reproduction, College of Animal Sciences, Jilin University, Changchun 130062, China
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5
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Buss JH, Lenz LS, Pereira LC, Torgo D, Marcolin J, Begnini KR, Lenz G. The role of mitosis in generating fitness heterogeneity. J Cell Sci 2023; 136:286224. [PMID: 36594556 DOI: 10.1242/jcs.260103] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/08/2022] [Accepted: 11/25/2022] [Indexed: 01/04/2023] Open
Abstract
Cancer cells have heterogeneous fitness, and this heterogeneity stems from genetic and epigenetic sources. Here, we sought to assess the contribution of asymmetric mitosis (AM) and time on the variability of fitness in sister cells. Around one quarter of sisters had differences in fitness, assessed as the intermitotic time (IMT), from 330 to 510 min. Phenotypes related to fitness, such as ERK activity (herein referring to ERK1 and ERK2, also known as MAPK3 and MAPK1, respectively), DNA damage and nuclear morphological phenotypes were also asymmetric at mitosis or turned asymmetric over the course of the cell cycle. The ERK activity of mother cell was found to influence the ERK activity and the IMT of the daughter cells, and cells with ERK asymmetry at mitosis produced more offspring with AMs, suggesting heritability of the AM phenotype for ERK activity. Our findings demonstrate how variabilities in sister cells can be generated, contributing to the phenotype heterogeneities in tumor cells.
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Affiliation(s)
- Julieti Huch Buss
- Departamento de Biofísica, Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS 91509-900, Brazil.,Centro de Biotecnologia, Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS 91509-900, Brazil
| | - Luana Suéling Lenz
- Departamento de Biofísica, Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS 91509-900, Brazil.,Centro de Biotecnologia, Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS 91509-900, Brazil
| | - Luiza Cherobini Pereira
- Departamento de Biofísica, Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS 91509-900, Brazil.,Centro de Biotecnologia, Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS 91509-900, Brazil
| | - Daphne Torgo
- Departamento de Biofísica, Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS 91509-900, Brazil.,Centro de Biotecnologia, Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS 91509-900, Brazil
| | - Júlia Marcolin
- Departamento de Biofísica, Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS 91509-900, Brazil.,Centro de Biotecnologia, Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS 91509-900, Brazil
| | - Karine Rech Begnini
- Departamento de Biofísica, Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS 91509-900, Brazil.,Centro de Biotecnologia, Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS 91509-900, Brazil
| | - Guido Lenz
- Departamento de Biofísica, Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS 91509-900, Brazil.,Centro de Biotecnologia, Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS 91509-900, Brazil
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6
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Sarma U, Ripka L, Anyaegbunam UA, Legewie S. Modeling Cellular Signaling Variability Based on Single-Cell Data: The TGFβ-SMAD Signaling Pathway. Methods Mol Biol 2023; 2634:215-251. [PMID: 37074581 DOI: 10.1007/978-1-0716-3008-2_10] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/20/2023]
Abstract
Nongenetic heterogeneity is key to cellular decisions, as even genetically identical cells respond in very different ways to the same external stimulus, e.g., during cell differentiation or therapeutic treatment of disease. Strong heterogeneity is typically already observed at the level of signaling pathways that are the first sensors of external inputs and transmit information to the nucleus where decisions are made. Since heterogeneity arises from random fluctuations of cellular components, mathematical models are required to fully describe the phenomenon and to understand the dynamics of heterogeneous cell populations. Here, we review the experimental and theoretical literature on cellular signaling heterogeneity, with special focus on the TGFβ/SMAD signaling pathway.
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Affiliation(s)
- Uddipan Sarma
- Institute of Molecular Biology (IMB), Mainz, Germany
| | - Lorenz Ripka
- Institute of Molecular Biology (IMB), Mainz, Germany
- Department of Systems Biology, Institute for Biomedical Genetics, University of Stuttgart, Stuttgart, Germany
| | - Uchenna Alex Anyaegbunam
- Institute of Molecular Biology (IMB), Mainz, Germany
- Department of Systems Biology, Institute for Biomedical Genetics, University of Stuttgart, Stuttgart, Germany
| | - Stefan Legewie
- Institute of Molecular Biology (IMB), Mainz, Germany.
- Department of Systems Biology, Institute for Biomedical Genetics, University of Stuttgart, Stuttgart, Germany.
- Stuttgart Research Center for Systems Biology, University of Stuttgart, Stuttgart, Germany.
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7
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Vittadello ST, Stumpf MPH. Open problems in mathematical biology. Math Biosci 2022; 354:108926. [PMID: 36377100 DOI: 10.1016/j.mbs.2022.108926] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/16/2022] [Revised: 10/21/2022] [Accepted: 10/21/2022] [Indexed: 11/06/2022]
Abstract
Biology is data-rich, and it is equally rich in concepts and hypotheses. Part of trying to understand biological processes and systems is therefore to confront our ideas and hypotheses with data using statistical methods to determine the extent to which our hypotheses agree with reality. But doing so in a systematic way is becoming increasingly challenging as our hypotheses become more detailed, and our data becomes more complex. Mathematical methods are therefore gaining in importance across the life- and biomedical sciences. Mathematical models allow us to test our understanding, make testable predictions about future behaviour, and gain insights into how we can control the behaviour of biological systems. It has been argued that mathematical methods can be of great benefit to biologists to make sense of data. But mathematics and mathematicians are set to benefit equally from considering the often bewildering complexity inherent to living systems. Here we present a small selection of open problems and challenges in mathematical biology. We have chosen these open problems because they are of both biological and mathematical interest.
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Affiliation(s)
- Sean T Vittadello
- Melbourne Integrative Genomics, University of Melbourne, Australia; School of BioSciences, University of Melbourne, Australia
| | - Michael P H Stumpf
- Melbourne Integrative Genomics, University of Melbourne, Australia; School of BioSciences, University of Melbourne, Australia; School of Mathematics and Statistics, University of Melbourne, Australia.
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8
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Towards 'end-to-end' analysis and understanding of biological timecourse data. Biochem J 2022; 479:1257-1263. [PMID: 35713413 PMCID: PMC9246344 DOI: 10.1042/bcj20220053] [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] [Received: 02/03/2022] [Revised: 05/19/2022] [Accepted: 05/20/2022] [Indexed: 11/17/2022]
Abstract
Petabytes of increasingly complex and multidimensional live cell and tissue imaging data are generated every year. These videos hold large promise for understanding biology at a deep and fundamental level, as they capture single-cell and multicellular events occurring over time and space. However, the current modalities for analysis and mining of these data are scattered and user-specific, preventing more unified analyses from being performed over different datasets and obscuring possible scientific insights. Here, we propose a unified pipeline for storage, segmentation, analysis, and statistical parametrization of live cell imaging datasets.
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9
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Diaz LPM, Stumpf MPH. HyperGraphs.jl - representing high-order relationships in Julia. Bioinformatics 2022; 38:3660-3661. [PMID: 35674360 PMCID: PMC9326852 DOI: 10.1093/bioinformatics/btac347] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/13/2021] [Revised: 05/10/2022] [Accepted: 06/01/2022] [Indexed: 11/14/2022] Open
Abstract
Summary HyperGraphs.jl is a Julia package that implements hypergraphs. These are a generalization of graphs that allow us to represent n-ary relationships and not just binary, pairwise relationships. High-order interactions are commonplace in biological systems and are of critical importance to their dynamics; hypergraphs thus offer a natural way to accurately describe and model these systems. Availability and implementation HyperGraphs.jl is freely available under the MIT license. Source code and documentation can be found at https://github.com/lpmdiaz/HyperGraphs.jl. Supplementary information Supplementary data are available at Bioinformatics online.
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Affiliation(s)
- Léo P M Diaz
- Melbourne Integrative Genomics and School of Mathematics and Statistics, University of Melbourne, Melbourne, Parkville, 3010, VIC, Australia
| | - Michael P H Stumpf
- Melbourne Integrative Genomics and School of Mathematics and Statistics, University of Melbourne, Melbourne, Parkville, 3010, VIC, Australia.,School of BioSciences, University of Melbourne, Melbourne, Parkville, 3010, VIC, Australia
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10
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microRNA-Mediated Encoding and Decoding of Time-Dependent Signals in Tumorigenesis. Biomolecules 2022; 12:biom12020213. [PMID: 35204714 PMCID: PMC8961662 DOI: 10.3390/biom12020213] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/22/2021] [Revised: 01/13/2022] [Accepted: 01/21/2022] [Indexed: 02/01/2023] Open
Abstract
microRNAs, pivotal post-transcriptional regulators of gene expression, in the past decades have caught the attention of researchers for their involvement in different biological processes, ranging from cell development to cancer. Although lots of effort has been devoted to elucidate the topological features and the equilibrium properties of microRNA-mediated motifs, little is known about how the information encoded in frequency, amplitude, duration, and other features of their regulatory signals can affect the resulting gene expression patterns. Here, we review the current knowledge about microRNA-mediated gene regulatory networks characterized by time-dependent input signals, such as pulses, transient inputs, and oscillations. First, we identify the general characteristic of the main motifs underlying temporal patterns. Then, we analyze their impact on two commonly studied oncogenic networks, showing how their dysfunction can lead to tumorigenesis.
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11
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Rommelfanger MK, MacLean AL. A single-cell resolved cell-cell communication model explains lineage commitment in hematopoiesis. Development 2021; 148:273837. [PMID: 34935903 PMCID: PMC8722395 DOI: 10.1242/dev.199779] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/03/2021] [Accepted: 11/06/2021] [Indexed: 01/29/2023]
Abstract
Cells do not make fate decisions independently. Arguably, every cell-fate decision occurs in response to environmental signals. In many cases, cell-cell communication alters the dynamics of the internal gene regulatory network of a cell to initiate cell-fate transitions, yet models rarely take this into account. Here, we have developed a multiscale perspective to study the granulocyte-monocyte versus megakaryocyte-erythrocyte fate decisions. This transition is dictated by the GATA1-PU.1 network: a classical example of a bistable cell-fate system. We show that, for a wide range of cell communication topologies, even subtle changes in signaling can have pronounced effects on cell-fate decisions. We go on to show how cell-cell coupling through signaling can spontaneously break the symmetry of a homogenous cell population. Noise, both intrinsic and extrinsic, shapes the decision landscape profoundly, and affects the transcriptional dynamics underlying this important hematopoietic cell-fate decision-making system. This article has an associated ‘The people behind the papers’ interview. Summary: Through theory and computational modeling, cell-cell communication is revealed to be a crucial and under-appreciated determinant of cell-fate decision-making during hematopoiesis.
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Affiliation(s)
- Megan K Rommelfanger
- Department of Quantitative and Computational Biology, University of Southern California, 1050 Childs Way, Los Angeles, CA 90089, USA
| | - Adam L MacLean
- Department of Quantitative and Computational Biology, University of Southern California, 1050 Childs Way, Los Angeles, CA 90089, USA
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12
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Ham L, Jackson M, Stumpf MPH. Pathway dynamics can delineate the sources of transcriptional noise in gene expression. eLife 2021; 10:e69324. [PMID: 34636320 PMCID: PMC8608387 DOI: 10.7554/elife.69324] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/12/2021] [Accepted: 10/11/2021] [Indexed: 11/25/2022] Open
Abstract
Single-cell expression profiling opens up new vistas on cellular processes. Extensive cell-to-cell variability at the transcriptomic and proteomic level has been one of the stand-out observations. Because most experimental analyses are destructive we only have access to snapshot data of cellular states. This loss of temporal information presents significant challenges for inferring dynamics, as well as causes of cell-to-cell variability. In particular, we typically cannot separate dynamic variability from within cells ('intrinsic noise') from variability across the population ('extrinsic noise'). Here, we make this non-identifiability mathematically precise, allowing us to identify new experimental set-ups that can assist in resolving this non-identifiability. We show that multiple generic reporters from the same biochemical pathways (e.g. mRNA and protein) can infer magnitudes of intrinsic and extrinsic transcriptional noise, identifying sources of heterogeneity. Stochastic simulations support our theory, and demonstrate that 'pathway-reporters' compare favourably to the well-known, but often difficult to implement, dual-reporter method.
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Affiliation(s)
- Lucy Ham
- School of BioSciences, University of MelbourneMelbourneAustralia
| | - Marcel Jackson
- Department of Mathematics and Statistics, La Trobe UniversityMelbourneAustralia
| | - Michael PH Stumpf
- School of Mathematics and Statistics, University of MelbourneMelbourneAustralia
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13
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Zheng Q, Chen X, Qiao C, Wang M, Chen W, Luan X, Yan Y, Shen C, Fang J, Hu X, Zheng B, Wu Y, Yu J. Somatic CG6015 mediates cyst stem cell maintenance and germline stem cell differentiation via EGFR signaling in Drosophila testes. Cell Death Discov 2021; 7:68. [PMID: 33824283 PMCID: PMC8024382 DOI: 10.1038/s41420-021-00452-w] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/05/2021] [Revised: 02/21/2021] [Accepted: 03/18/2021] [Indexed: 11/09/2022] Open
Abstract
Stem cell niche is regulated by intrinsic and extrinsic factors. In the Drosophila testis, cyst stem cells (CySCs) support the differentiation of germline stem cells (GSCs). However, the underlying mechanisms remain unclear. In this study, we found that somatic CG6015 is required for CySC maintenance and GSC differentiation in a Drosophila model. Knockdown of CG6015 in CySCs caused aberrant activation of dpERK in undifferentiated germ cells in the Drosophila testis, and disruption of key downstream targets of EGFR signaling (Dsor1 and rl) in CySCs results in a phenotype resembling that of CG6015 knockdown. CG6015, Dsor1, and rl are essential for the survival of Drosophila cell line Schneider 2 (S2) cells. Our data showed that somatic CG6015 regulates CySC maintenance and GSC differentiation via EGFR signaling, and inhibits aberrant activation of germline dpERK signals. These findings indicate regulatory mechanisms of stem cell niche homeostasis in the Drosophila testis.
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Affiliation(s)
- Qianwen Zheng
- Department of Gynecology, the Affiliated Hospital of Jiangsu University, Jiangsu University, 212001, Zhenjiang, Jiangsu, P.R. China
| | - Xia Chen
- Department of Gynecology, the Affiliated Hospital of Jiangsu University, Jiangsu University, 212001, Zhenjiang, Jiangsu, P.R. China
| | - Chen Qiao
- Department of Clinical Pharmacy, the Affiliated Hospital of Jiangsu University, Jiangsu University, 212001, Zhenjiang, Jiangsu, P.R. China
| | - Min Wang
- Department of Gynecology, the Affiliated Hospital of Jiangsu University, Jiangsu University, 212001, Zhenjiang, Jiangsu, P.R. China
| | - Wanyin Chen
- Department of Gynecology, the Affiliated Hospital of Jiangsu University, Jiangsu University, 212001, Zhenjiang, Jiangsu, P.R. China
| | - Xiaojin Luan
- Department of Gynecology, the Affiliated Hospital of Jiangsu University, Jiangsu University, 212001, Zhenjiang, Jiangsu, P.R. China
| | - Yidan Yan
- Department of Gynecology, the Affiliated Hospital of Jiangsu University, Jiangsu University, 212001, Zhenjiang, Jiangsu, P.R. China
| | - Cong Shen
- State Key Laboratory of Reproductive Medicine, Center for Reproduction and Genetics, Suzhou Municipal Hospital, The Affiliated Suzhou Hospital of Nanjing Medical University, Gusu School, Nanjing Medical University, 215002, Suzhou, Jiangsu, P.R. China
| | - Jie Fang
- Department of Gynecology, the Affiliated Hospital of Jiangsu University, Jiangsu University, 212001, Zhenjiang, Jiangsu, P.R. China
| | - Xing Hu
- Department of Gynecology, the Affiliated Hospital of Jiangsu University, Jiangsu University, 212001, Zhenjiang, Jiangsu, P.R. China
| | - Bo Zheng
- State Key Laboratory of Reproductive Medicine, Center for Reproduction and Genetics, Suzhou Municipal Hospital, The Affiliated Suzhou Hospital of Nanjing Medical University, Gusu School, Nanjing Medical University, 215002, Suzhou, Jiangsu, P.R. China.
| | - Yibo Wu
- Human Reproductive and Genetic Center, Affiliated Hospital of Jiangnan University, 214062, Wuxi, Jiangsu, P.R. China.
| | - Jun Yu
- Department of Gynecology, the Affiliated Hospital of Jiangsu University, Jiangsu University, 212001, Zhenjiang, Jiangsu, P.R. China.
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14
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Deshmukh S, Saini S. Phenotypic Heterogeneity in Tumor Progression, and Its Possible Role in the Onset of Cancer. Front Genet 2020; 11:604528. [PMID: 33329751 PMCID: PMC7734151 DOI: 10.3389/fgene.2020.604528] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/09/2020] [Accepted: 11/10/2020] [Indexed: 12/20/2022] Open
Abstract
Heterogeneity among isogenic cells/individuals has been known for at least 150 years. Even Mendel, working on pea plants, realized that not all tall plants were identical. However, Mendel was more interested in the discontinuous variation between genetically distinct individuals. The concept of environment dictating distinct phenotypes among isogenic individuals has since been shown to impact the evolution of populations in numerous examples at different scales of life. In this review, we discuss how phenotypic heterogeneity and its evolutionary implications exist at all levels of life, from viruses to mammals. In particular, we discuss how a particular disease condition (cancer) is impacted by heterogeneity among isogenic cells, and propose a potential role that phenotypic heterogeneity might play toward the onset of the disease.
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Affiliation(s)
- Saniya Deshmukh
- Department of Chemical Engineering, Indian Institute of Technology Bombay, Mumbai, India
| | - Supreet Saini
- Department of Chemical Engineering, Indian Institute of Technology Bombay, Mumbai, India
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15
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Miyagi H, Hiroshima M, Sako Y. Cell-to-cell diversification in ERBB-RAS-MAPK signal transduction that produces cell-type specific growth factor responses. Biosystems 2020; 199:104293. [PMID: 33221378 DOI: 10.1016/j.biosystems.2020.104293] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/28/2020] [Revised: 11/12/2020] [Accepted: 11/14/2020] [Indexed: 02/06/2023]
Abstract
Growth factors regulate cell fates, including their proliferation, differentiation, survival, and death, according to the cell type. Even when the response to a specific growth factor is deterministic for collective cell behavior, significant levels of fluctuation are often observed between single cells. Statistical analyses of single-cell responses provide insights into the mechanism of cell fate decisions but very little is known about the distributions of the internal states of cells responding to growth factors. Using multi-color immunofluorescent staining, we have here detected the phosphorylation of seven elements in the early response of the ERBB-RAS-MAPK system to two growth factors. Among these seven elements, five were analyzed simultaneously in distinct combinations in the same single cells. Although principle component analysis suggested cell-type and input specific phosphorylation patterns, cell-to-cell fluctuation was large. Mutual information analysis suggested that each cell type uses multitrack (bush-like) signal transduction pathways under conditions in which clear fate changes have been reported. The clustering of single-cell response patterns indicated that the fate change in a cell population correlates with the large entropy of the response, suggesting a bet-hedging strategy is used in decision making. A comparison of true and randomized datasets further indicated that this large variation is not produced by simple reaction noise, but is defined by the properties of the signal-processing network.
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Affiliation(s)
- Hiraku Miyagi
- Cellular Informatics Laboratory, RIKEN, Cluster for Pioneering Research, 2-1, Hirosawa, Wako, 351-0198, Japan; CREST, JST, 4-1-8, Honcho, Kawaguchi, 332-0012, Japan
| | - Michio Hiroshima
- Cellular Informatics Laboratory, RIKEN, Cluster for Pioneering Research, 2-1, Hirosawa, Wako, 351-0198, Japan; CREST, JST, 4-1-8, Honcho, Kawaguchi, 332-0012, Japan; Laboratory for Cell Signaling Dynamics, RIKEN, Center for Biosystems Dynamics Research, 6-2-3, Furuedai, Suita, 565-0874, Japan
| | - Yasushi Sako
- Cellular Informatics Laboratory, RIKEN, Cluster for Pioneering Research, 2-1, Hirosawa, Wako, 351-0198, Japan; CREST, JST, 4-1-8, Honcho, Kawaguchi, 332-0012, Japan.
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16
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Yeung E, McFann S, Marsh L, Dufresne E, Filippi S, Harrington HA, Shvartsman SY, Wühr M. Inference of Multisite Phosphorylation Rate Constants and Their Modulation by Pathogenic Mutations. Curr Biol 2020; 30:877-882.e6. [PMID: 32059766 PMCID: PMC7085240 DOI: 10.1016/j.cub.2019.12.052] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/07/2019] [Revised: 11/03/2019] [Accepted: 12/16/2019] [Indexed: 01/03/2023]
Abstract
Multisite protein phosphorylation plays a critical role in cell regulation [1-3]. It is widely appreciated that the functional capabilities of multisite phosphorylation depend on the order and kinetics of phosphorylation steps, but kinetic aspects of multisite phosphorylation remain poorly understood [4-6]. Here, we focus on what appears to be the simplest scenario, when a protein is phosphorylated on only two sites in a strict, well-defined order. This scenario describes the activation of ERK, a highly conserved cell-signaling enzyme. We use Bayesian parameter inference in a structurally identifiable kinetic model to dissect dual phosphorylation of ERK by MEK, a kinase that is mutated in a large number of human diseases [7-12]. Our results reveal how enzyme processivity and efficiencies of individual phosphorylation steps are altered by pathogenic mutations. The presented approach, which connects specific mutations to kinetic parameters of multisite phosphorylation mechanisms, provides a systematic framework for closing the gap between studies with purified enzymes and their effects in the living organism.
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Affiliation(s)
- Eyan Yeung
- Lewis-Sigler Institute for Integrative Genomics, Princeton University, Carl Icahn Laboratory, Washington Road, Princeton, NJ 08544, USA; Department of Molecular Biology, Princeton University, Lewis Thomas Laboratory, Washington Road, Princeton, NJ 08544, USA
| | - Sarah McFann
- Lewis-Sigler Institute for Integrative Genomics, Princeton University, Carl Icahn Laboratory, Washington Road, Princeton, NJ 08544, USA; Department of Chemical and Biological Engineering, Engineering Quad, Princeton University, Princeton, NJ 08544, USA
| | - Lewis Marsh
- Mathematical Institute, University of Oxford, Andrew Wiles Building, Woodstock Road, Oxford OX2 6GG, UK
| | - Emilie Dufresne
- Department of Mathematics, James College, Campus West, University of York, York YO10 5DD, UK
| | - Sarah Filippi
- Department of Epidemiology and Biostatistics, Imperial College London, Medical School Building, St Mary's Campus, Norfolk Place, London W2 1PG, UK; Department of Mathematics, South Kensington Campus, Imperial College London, London SW7 2AZ, UK
| | - Heather A Harrington
- Mathematical Institute, University of Oxford, Andrew Wiles Building, Woodstock Road, Oxford OX2 6GG, UK
| | - Stanislav Y Shvartsman
- Lewis-Sigler Institute for Integrative Genomics, Princeton University, Carl Icahn Laboratory, Washington Road, Princeton, NJ 08544, USA; Department of Molecular Biology, Princeton University, Lewis Thomas Laboratory, Washington Road, Princeton, NJ 08544, USA; Flatiron Institute, Simons Foundation, New York, NY 10010, USA.
| | - Martin Wühr
- Lewis-Sigler Institute for Integrative Genomics, Princeton University, Carl Icahn Laboratory, Washington Road, Princeton, NJ 08544, USA; Department of Molecular Biology, Princeton University, Lewis Thomas Laboratory, Washington Road, Princeton, NJ 08544, USA.
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17
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Information Theory: New Look at Oncogenic Signaling Pathways. Trends Cell Biol 2019; 29:862-875. [DOI: 10.1016/j.tcb.2019.08.005] [Citation(s) in RCA: 16] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/28/2019] [Revised: 08/09/2019] [Accepted: 08/13/2019] [Indexed: 12/23/2022]
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18
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Information-theoretic analysis of multivariate single-cell signaling responses. PLoS Comput Biol 2019; 15:e1007132. [PMID: 31299056 PMCID: PMC6655862 DOI: 10.1371/journal.pcbi.1007132] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/19/2018] [Revised: 07/24/2019] [Accepted: 05/23/2019] [Indexed: 12/20/2022] Open
Abstract
Mathematical methods of information theory appear to provide a useful language to describe how stimuli are encoded in activities of signaling effectors. Exploring the information-theoretic perspective, however, remains conceptually, experimentally and computationally challenging. Specifically, existing computational tools enable efficient analysis of relatively simple systems, usually with one input and output only. Moreover, their robust and readily applicable implementations are missing. Here, we propose a novel algorithm, SLEMI—statistical learning based estimation of mutual information, to analyze signaling systems with high-dimensional outputs and a large number of input values. Our approach is efficient in terms of computational time as well as sample size needed for accurate estimation. Analysis of the NF-κB single—cell signaling responses to TNF-α reveals that NF-κB signaling dynamics improves discrimination of high concentrations of TNF-α with a relatively modest impact on discrimination of low concentrations. Provided R-package allows the approach to be used by computational biologists with only elementary knowledge of information theory. In light of single-cell, live-imaging experiments understanding of how cells transmit information about identity and quantity of stimuli is incomplete. When exposed to the same stimulus individual cells exhibit substantial cell-to-cell heterogeneity. Besides, stimuli have been shown to regulate temporal profiles of signaling effectors. Therefore, it is, for instance, not entirely clear whether single-cell responses are binary or contain more information about the quantity of stimuli. The above questions resulted in a considerable interest to study cellular signaling within the framework of information theory. Unfortunately, the utilization of the information-theoretic perspective is handicapped in part by the lack of suitable methods that account for multivariate signaling data. Here, we propose a novel algorithm that breaks a considerable computational barrier by allowing the effective information-theoretic analysis of highly-dimensional single-cell measurements. Our approach is computationally efficient, robust and straightforward to use. Moreover, we provide a simple R-package implementation.
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19
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A Simple and Flexible Computational Framework for Inferring Sources of Heterogeneity from Single-Cell Dynamics. Cell Syst 2019; 8:15-26.e11. [PMID: 30638813 DOI: 10.1016/j.cels.2018.12.007] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2018] [Revised: 10/16/2018] [Accepted: 12/11/2018] [Indexed: 01/26/2023]
Abstract
Single-cell time-lapse data provide the means for disentangling sources of cell-to-cell and intra-cellular variability, a key step for understanding heterogeneity in cell populations. However, single-cell analysis with dynamic models is a challenging open problem: current inference methods address only single-gene expression or neglect parameter correlations. We report on a simple, flexible, and scalable method for estimating cell-specific and population-average parameters of non-linear mixed-effects models of cellular networks, demonstrating its accuracy with a published model and dataset. We also propose sensitivity analysis for identifying which biological sub-processes quantitatively and dynamically contribute to cell-to-cell variability. Our application to endocytosis in yeast demonstrates that dynamic models of realistic size can be developed for the analysis of single-cell data and that shifting the focus from single reactions or parameters to nuanced and time-dependent contributions of sub-processes helps biological interpretation. Generality and simplicity of the approach will facilitate customized extensions for analyzing single-cell dynamics.
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20
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Mitra T, Menon SN, Sinha S. Emergent memory in cell signaling: Persistent adaptive dynamics in cascades can arise from the diversity of relaxation time-scales. Sci Rep 2018; 8:13230. [PMID: 30185923 PMCID: PMC6125488 DOI: 10.1038/s41598-018-31626-9] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/02/2018] [Accepted: 08/23/2018] [Indexed: 12/13/2022] Open
Abstract
The mitogen-activated protein kinase (MAPK) signaling cascade, an evolutionarily conserved motif present in all eukaryotic cells, is involved in coordinating crucial cellular functions. While the asymptotic dynamical behavior of the pathway stimulated by a time-invariant signal is relatively well-understood, we show using a computational model that it exhibits a rich repertoire of transient adaptive responses to changes in stimuli. When the signal is switched on, the response is characterized by long-lived modulations in frequency as well as amplitude. On withdrawing the stimulus, the activity decays over long timescales, exhibiting reverberations characterized by repeated spiking in the activated MAPK concentration. The long-term persistence of such post-stimulus activity suggests that the cascade retains memory of the signal for a significant duration following its removal. The molecular mechanism underlying the reverberatory activity is related to the existence of distinct relaxation rates for the different cascade components. This results in the imbalance of fluxes between different layers of the cascade, with the reuse of activated kinases as enzymes when they are released from sequestration in complexes. The persistent adaptive response, indicative of a cellular “short-term” memory, suggests that this ubiquitous signaling pathway plays an even more central role in information processing by eukaryotic cells.
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Affiliation(s)
- Tanmay Mitra
- The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai, 600113, India.,Homi Bhabha National Institute, Anushaktinagar, Mumbai, 400094, India
| | - Shakti N Menon
- The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai, 600113, India
| | - Sitabhra Sinha
- The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai, 600113, India. .,Homi Bhabha National Institute, Anushaktinagar, Mumbai, 400094, India.
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21
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Brackston RD, Lakatos E, Stumpf MPH. Transition state characteristics during cell differentiation. PLoS Comput Biol 2018; 14:e1006405. [PMID: 30235202 PMCID: PMC6168170 DOI: 10.1371/journal.pcbi.1006405] [Citation(s) in RCA: 27] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/23/2018] [Revised: 10/02/2018] [Accepted: 07/27/2018] [Indexed: 12/11/2022] Open
Abstract
Models describing the process of stem-cell differentiation are plentiful, and may offer insights into the underlying mechanisms and experimentally observed behaviour. Waddington's epigenetic landscape has been providing a conceptual framework for differentiation processes since its inception. It also allows, however, for detailed mathematical and quantitative analyses, as the landscape can, at least in principle, be related to mathematical models of dynamical systems. Here we focus on a set of dynamical systems features that are intimately linked to cell differentiation, by considering exemplar dynamical models that capture important aspects of stem cell differentiation dynamics. These models allow us to map the paths that cells take through gene expression space as they move from one fate to another, e.g. from a stem-cell to a more specialized cell type. Our analysis highlights the role of the transition state (TS) that separates distinct cell fates, and how the nature of the TS changes as the underlying landscape changes-change that can be induced by e.g. cellular signaling. We demonstrate that models for stem cell differentiation may be interpreted in terms of either a static or transitory landscape. For the static case the TS represents a particular transcriptional profile that all cells approach during differentiation. Alternatively, the TS may refer to the commonly observed period of heterogeneity as cells undergo stochastic transitions.
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Affiliation(s)
- Rowan D. Brackston
- Centre for Integrative Systems Biology and Bioinformatics, Department of Life Sciences, Imperial College London, London, United Kingdom
| | - Eszter Lakatos
- Centre for Integrative Systems Biology and Bioinformatics, Department of Life Sciences, Imperial College London, London, United Kingdom
| | - Michael P. H. Stumpf
- Centre for Integrative Systems Biology and Bioinformatics, Department of Life Sciences, Imperial College London, London, United Kingdom
- School of BioScience and School of Mathematics and Statistics, University of Melbourne, Melbourne, Australia
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22
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Kubota H, Uda S, Matsuzaki F, Yamauchi Y, Kuroda S. In Vivo Decoding Mechanisms of the Temporal Patterns of Blood Insulin by the Insulin-AKT Pathway in the Liver. Cell Syst 2018; 7:118-128.e3. [PMID: 29960883 DOI: 10.1016/j.cels.2018.05.013] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/14/2017] [Revised: 04/06/2018] [Accepted: 05/18/2018] [Indexed: 10/28/2022]
Abstract
Cells respond to various extracellular stimuli through a limited number of signaling pathways. One strategy to process such stimuli is to code the information into the temporal patterns of molecules. Although we showed that insulin selectively regulated molecules depending on its temporal patterns using Fao cells, the in vivo mechanism remains unknown. Here, we show how the insulin-AKT pathway processes the information encoded into the temporal patterns of blood insulin. We performed hyperinsulinemic-euglycemic clamp experiments and found that, in the liver, all temporal patterns of insulin are encoded into the insulin receptor, and downstream molecules selectively decode them through AKT. S6K selectively decodes the additional secretion information. G6Pase interprets the basal secretion information through FoxO1, while GSK3β decodes all secretion pattern information. Mathematical modeling revealed the mechanism via differences in network structures and from sensitivity and time constants. Given that almost all hormones exhibit distinct temporal patterns, temporal coding may be a general principle of system homeostasis by hormones.
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Affiliation(s)
- Hiroyuki Kubota
- Division of Integrated Omics, Research Center for Transomics Medicine, Medical Institute of Bioregulation, Kyushu University, 3-1-1 Maidashi, Higashi-ku, Fukuoka, Fukuoka 812-8582, Japan; PRESTO, Japan Science and Technology Agency, Higashi-ku, Fukuoka, Fukuoka 812-8582, Japan.
| | - Shinsuke Uda
- Division of Integrated Omics, Research Center for Transomics Medicine, Medical Institute of Bioregulation, Kyushu University, 3-1-1 Maidashi, Higashi-ku, Fukuoka, Fukuoka 812-8582, Japan
| | - Fumiko Matsuzaki
- Division of Integrated Omics, Research Center for Transomics Medicine, Medical Institute of Bioregulation, Kyushu University, 3-1-1 Maidashi, Higashi-ku, Fukuoka, Fukuoka 812-8582, Japan
| | - Yukiyo Yamauchi
- Division of Integrated Omics, Research Center for Transomics Medicine, Medical Institute of Bioregulation, Kyushu University, 3-1-1 Maidashi, Higashi-ku, Fukuoka, Fukuoka 812-8582, Japan
| | - Shinya Kuroda
- Department of Biological Sciences, Graduate School of Science, University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan; CREST, Japan Science and Technology Corporation, Bunkyo-ku, Tokyo 113-0033, Japan.
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23
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Loos C, Moeller K, Fröhlich F, Hucho T, Hasenauer J. A Hierarchical, Data-Driven Approach to Modeling Single-Cell Populations Predicts Latent Causes of Cell-To-Cell Variability. Cell Syst 2018; 6:593-603.e13. [DOI: 10.1016/j.cels.2018.04.008] [Citation(s) in RCA: 29] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/17/2017] [Revised: 09/28/2017] [Accepted: 04/10/2018] [Indexed: 12/23/2022]
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24
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Mean-Independent Noise Control of Cell Fates via Intermediate States. iScience 2018; 3:11-20. [PMID: 30428314 PMCID: PMC6137274 DOI: 10.1016/j.isci.2018.04.002] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/28/2017] [Revised: 02/21/2018] [Accepted: 03/09/2018] [Indexed: 11/24/2022] Open
Abstract
Stochasticity affects accurate signal detection and robust generation of correct cell fates. Although many known regulatory mechanisms may reduce fluctuations in signals, most simultaneously influence their mean dynamics, leading to unfaithful cell fates. Through analysis and computation, we demonstrate that a reversible signaling mechanism acting through intermediate states can reduce noise while maintaining the mean. This mean-independent noise control (MINC) mechanism is investigated in the context of an intracellular binding protein that regulates retinoic acid (RA) signaling during zebrafish hindbrain development. By comparing our models with experimental data, we find that the MINC mechanism allows for sharp boundaries of gene expression without sacrificing boundary accuracy. In addition, this MINC mechanism can modulate noise to levels that we show are beneficial to spatial patterning through noise-induced cell fate switching. These results reveal a design principle that may be important for noise regulation in many systems that control cell fate determination. Mean-independent noise control allows noise attenuation without affecting the mean Intermediate states enable such control through proportional coupling This controls spatial gene expression noise without shifting boundary locations Specific noise levels are required for successful downstream boundary sharpening
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25
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Computational Methods for Estimating Molecular System from Membrane Potential Recordings in Nerve Growth Cone. Sci Rep 2018. [PMID: 29540815 PMCID: PMC5852145 DOI: 10.1038/s41598-018-22506-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022] Open
Abstract
Biological cells express intracellular biomolecular information to the extracellular environment as various physical responses. We show a novel computational approach to estimate intracellular biomolecular pathways from growth cone electrophysiological responses. Previously, it was shown that cGMP signaling regulates membrane potential (MP) shifts that control the growth cone turning direction during neuronal development. We present here an integrated deterministic mathematical model and Bayesian reversed-engineering framework that enables estimation of the molecular signaling pathway from electrical recordings and considers both the system uncertainty and cell-to-cell variability. Our computational method selects the most plausible molecular pathway from multiple candidates while satisfying model simplicity and considering all possible parameter ranges. The model quantitatively reproduces MP shifts depending on cGMP levels and MP variability potential in different experimental conditions. Lastly, our model predicts that chloride channel inhibition by cGMP-dependent protein kinase (PKG) is essential in the core system for regulation of the MP shifts.
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26
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Voliotis M, Garner KL, Alobaid H, Tsaneva-Atanasova K, McArdle CA. Gonadotropin-releasing hormone signaling: An information theoretic approach. Mol Cell Endocrinol 2018; 463:106-115. [PMID: 28760599 DOI: 10.1016/j.mce.2017.07.028] [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] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 04/06/2017] [Revised: 07/27/2017] [Accepted: 07/27/2017] [Indexed: 12/16/2022]
Abstract
Gonadotropin-releasing hormone (GnRH) is a peptide hormone that mediates central control of reproduction, acting via G-protein coupled receptors that are primarily Gq coupled and mediate GnRH effects on the synthesis and secretion of luteinizing hormone and follicle-stimulating hormone. A great deal is known about the GnRH receptor signaling network but GnRH is secreted in short pulses and much less is known about how gonadotropes decode this pulsatile signal. Similarly, single cell measures reveal considerable cell-cell heterogeneity in responses to GnRH but the impact of this variability on signaling is largely unknown. Ordinary differential equation-based mathematical models have been used to explore the decoding of pulse dynamics and information theory-derived statistical measures are increasingly used to address the influence of cell-cell variability on the amount of information transferred by signaling pathways. Here, we describe both approaches for GnRH signaling, with emphasis on novel insights gained from the information theoretic approach and on the fundamental question of why GnRH is secreted in pulses.
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Affiliation(s)
- Margaritis Voliotis
- Department of Mathematics and Living Systems Institute, College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter, EX4 4QF, UK
| | - Kathryn L Garner
- Laboratories for Integrative Neuroscience and Endocrinology, School of Clinical Sciences, University of Bristol, Whitson Street, Bristol, BS1 3NY, UK
| | - Hussah Alobaid
- Laboratories for Integrative Neuroscience and Endocrinology, School of Clinical Sciences, University of Bristol, Whitson Street, Bristol, BS1 3NY, UK
| | - Krasimira Tsaneva-Atanasova
- Department of Mathematics and Living Systems Institute, College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter, EX4 4QF, UK; EPSRC Centre for Predictive Modeling in Healthcare, University of Exeter, Exeter, EX4 4QF, UK
| | - Craig A McArdle
- Laboratories for Integrative Neuroscience and Endocrinology, School of Clinical Sciences, University of Bristol, Whitson Street, Bristol, BS1 3NY, UK.
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27
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Folguera-Blasco N, Cuyàs E, Menéndez JA, Alarcón T. Epigenetic regulation of cell fate reprogramming in aging and disease: A predictive computational model. PLoS Comput Biol 2018; 14:e1006052. [PMID: 29543808 PMCID: PMC5871006 DOI: 10.1371/journal.pcbi.1006052] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/28/2017] [Revised: 03/27/2018] [Accepted: 02/21/2018] [Indexed: 01/12/2023] Open
Abstract
Understanding the control of epigenetic regulation is key to explain and modify the aging process. Because histone-modifying enzymes are sensitive to shifts in availability of cofactors (e.g. metabolites), cellular epigenetic states may be tied to changing conditions associated with cofactor variability. The aim of this study is to analyse the relationships between cofactor fluctuations, epigenetic landscapes, and cell state transitions. Using Approximate Bayesian Computation, we generate an ensemble of epigenetic regulation (ER) systems whose heterogeneity reflects variability in cofactor pools used by histone modifiers. The heterogeneity of epigenetic metabolites, which operates as regulator of the kinetic parameters promoting/preventing histone modifications, stochastically drives phenotypic variability. The ensemble of ER configurations reveals the occurrence of distinct epi-states within the ensemble. Whereas resilient states maintain large epigenetic barriers refractory to reprogramming cellular identity, plastic states lower these barriers, and increase the sensitivity to reprogramming. Moreover, fine-tuning of cofactor levels redirects plastic epigenetic states to re-enter epigenetic resilience, and vice versa. Our ensemble model agrees with a model of metabolism-responsive loss of epigenetic resilience as a cellular aging mechanism. Our findings support the notion that cellular aging, and its reversal, might result from stochastic translation of metabolic inputs into resilient/plastic cell states via ER systems.
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Affiliation(s)
- Núria Folguera-Blasco
- Centre de Recerca Matemàtica, Edifici C, Campus de Bellaterra, Bellaterra (Barcelona), Spain
- Departament de Matemàtiques, Universitat Autònoma de Barcelona, Bellaterra (Barcelona), Spain
| | - Elisabet Cuyàs
- Molecular Oncology Group, Girona Biomedical Research Institute (IDIBGI), Girona, Spain
- MetaboStem, Barcelona, Spain
| | - Javier A. Menéndez
- Molecular Oncology Group, Girona Biomedical Research Institute (IDIBGI), Girona, Spain
- MetaboStem, Barcelona, Spain
- ProCURE (Program Against Cancer Therapeutic Resistance), Metabolism and Cancer Group, Catalan Institute of Oncology, Girona, Spain
| | - Tomás Alarcón
- Centre de Recerca Matemàtica, Edifici C, Campus de Bellaterra, Bellaterra (Barcelona), Spain
- Departament de Matemàtiques, Universitat Autònoma de Barcelona, Bellaterra (Barcelona), Spain
- ICREA, Pg. Lluís Companys 23, Barcelona, Spain
- Barcelona Graduate School of Mathematics (BGSMath), Barcelona, Spain
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28
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Erez A, Vogel R, Mugler A, Belmonte A, Altan-Bonnet G. Modeling of cytometry data in logarithmic space: When is a bimodal distribution not bimodal? Cytometry A 2018; 93:611-619. [PMID: 29451717 DOI: 10.1002/cyto.a.23333] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/31/2017] [Revised: 11/17/2017] [Accepted: 01/12/2018] [Indexed: 11/05/2022]
Abstract
Recent efforts in systems immunology lead researchers to build quantitative models of cell activation and differentiation. One goal is to account for the distributions of proteins from single-cell measurements by flow cytometry or mass cytometry as readout of biological regulation. In that context, large cell-to-cell variability is often observed in biological quantities. We show here that these readouts, viewed in logarithmic scale may result in two easily-distinguishable modes, while the underlying distribution (in linear scale) is unimodal. We introduce a simple mathematical test to highlight this mismatch. We then dissect the flow of influence of cell-to-cell variability proposing a graphical model which motivates higher-dimensional analysis of the data. Finally we show how acquiring additional biological information can be used to reduce uncertainty introduced by cell-to-cell variability, helping to clarify whether the data is uni- or bimodal. This communication has cautionary implications for manual and automatic gating strategies, as well as clustering and modeling of single-cell measurements. © 2018 International Society for Advancement of Cytometry.
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Affiliation(s)
- Amir Erez
- Immunodynamics Group, Cancer and Inflammation Program, National Cancer Institute, National Institutes of Health, Bethesda, Maryland 20814
| | - Robert Vogel
- IBM T. J. Watson Research Center, Yorktown Heights, New York, New York 10598
| | - Andrew Mugler
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907
| | - Andrew Belmonte
- Immunodynamics Group, Cancer and Inflammation Program, National Cancer Institute, National Institutes of Health, Bethesda, Maryland 20814.,Department of Mathematics, Pennsylvania State University, University Park, Pennsylvania, 16802
| | - Grégoire Altan-Bonnet
- Immunodynamics Group, Cancer and Inflammation Program, National Cancer Institute, National Institutes of Health, Bethesda, Maryland 20814
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Saidak Z, Giacobbi AS, Morisse MC, Mammeri Y, Galmiche A. [Mathematical modeling: an essential tool for the study of therapeutic targeting in solid tumors]. Med Sci (Paris) 2017; 33:1055-1062. [PMID: 29261493 DOI: 10.1051/medsci/20173312012] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022] Open
Abstract
Recent progress in biology has made the study of the medical treatment of cancer more effective, but it has also revealed the large complexity of carcinogenesis and cell signaling. For many types of cancer, several therapeutic targets are known and in some cases drugs against these targets exist. Unfortunately, the target proteins often work in networks, resulting in functional adaptation and the development of resilience/resistance to medical treatment. The use of mathematical modeling makes it possible to carry out system-level analyses for improved study of therapeutic targeting in solid tumours. We present the main types of mathematical models used in cancer research and we provide examples illustrating the relevance of these approaches in molecular oncobiology.
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Affiliation(s)
- Zuzana Saidak
- Laboratoire d'oncobiologie moléculaire, Centre de biologie humaine (CBH), CHU Amiens Sud, Amiens, France
| | - Anne-Sophie Giacobbi
- Laboratoire amiénois de mathématique fondamentale et appliquée (LAMFA), CNRS UMR7352, UFR des sciences, Université de Picardie Jules Verne, Amiens, France
| | - Mony Chenda Morisse
- Laboratoire de biochimie, Centre de biologie humaine (CBH), CHU Amiens Sud, Amiens, France
| | - Youcef Mammeri
- Laboratoire amiénois de mathématique fondamentale et appliquée (LAMFA), CNRS UMR7352, UFR des sciences, Université de Picardie Jules Verne, Amiens, France
| | - Antoine Galmiche
- Laboratoire de biochimie, Centre de biologie humaine (CBH), CHU Amiens Sud, Amiens, France - Équipe CHIMERE (Chirurgie et extrémité céphalique, caractérisation morphologique et fonctionnelle), Université de Picardie Jules Verne, Amiens, France
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30
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Tsuchiya T, Fujii M, Matsuda N, Kunida K, Uda S, Kubota H, Konishi K, Kuroda S. System identification of signaling dependent gene expression with different time-scale data. PLoS Comput Biol 2017; 13:e1005913. [PMID: 29281625 PMCID: PMC5760096 DOI: 10.1371/journal.pcbi.1005913] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/24/2017] [Revised: 01/09/2018] [Accepted: 12/01/2017] [Indexed: 01/11/2023] Open
Abstract
Cells decode information of signaling activation at a scale of tens of minutes by downstream gene expression with a scale of hours to days, leading to cell fate decisions such as cell differentiation. However, no system identification method with such different time scales exists. Here we used compressed sensing technology and developed a system identification method using data of different time scales by recovering signals of missing time points. We measured phosphorylation of ERK and CREB, immediate early gene expression products, and mRNAs of decoder genes for neurite elongation in PC12 cell differentiation and performed system identification, revealing the input-output relationships between signaling and gene expression with sensitivity such as graded or switch-like response and with time delay and gain, representing signal transfer efficiency. We predicted and validated the identified system using pharmacological perturbation. Thus, we provide a versatile method for system identification using data with different time scales.
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Affiliation(s)
- Takaho Tsuchiya
- Department of Biological Sciences, Graduate School of Science, University of Tokyo, Tokyo, Japan
| | - Masashi Fujii
- Department of Biological Sciences, Graduate School of Science, University of Tokyo, Tokyo, Japan
- Molecular Genetics Research Laboratory, Graduate School of Science, University of Tokyo, Tokyo, Japan
| | - Naoki Matsuda
- Department of Biological Sciences, Graduate School of Science, University of Tokyo, Tokyo, Japan
| | - Katsuyuki Kunida
- Department of Biological Sciences, Graduate School of Science, University of Tokyo, Tokyo, Japan
- Laboratory of Computational Biology, Graduate School of Biological Sciences, Nara Institute of Science and Technology, Ikoma, Japan
| | - Shinsuke Uda
- Division of Integrated Omics, Research Center for Transomics Medicine, Medical Institute of Bioregulation, Kyushu University, Fukuoka, Japan
| | - Hiroyuki Kubota
- Division of Integrated Omics, Research Center for Transomics Medicine, Medical Institute of Bioregulation, Kyushu University, Fukuoka, Japan
| | - Katsumi Konishi
- Department of Computer Science, Faculty of Informatics, Kogakuin University, Tokyo, Japan
| | - Shinya Kuroda
- Department of Biological Sciences, Graduate School of Science, University of Tokyo, Tokyo, Japan
- CREST, Japan Science and Technology Corporation, Tokyo, Japan
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Chiang CK, Tworak A, Kevany BM, Xu B, Mayne J, Ning Z, Figeys D, Palczewski K. Quantitative phosphoproteomics reveals involvement of multiple signaling pathways in early phagocytosis by the retinal pigmented epithelium. J Biol Chem 2017; 292:19826-19839. [PMID: 28978645 DOI: 10.1074/jbc.m117.812677] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/16/2017] [Revised: 09/22/2017] [Indexed: 12/12/2022] Open
Abstract
One of the major biological functions of the retinal pigmented epithelium (RPE) is the clearance of shed photoreceptor outer segments (POS) through a multistep process resembling phagocytosis. RPE phagocytosis helps maintain the viability of photoreceptors that otherwise could succumb to the high metabolic flux and photo-oxidative stress associated with visual processing. The regulatory mechanisms underlying phagocytosis in the RPE are not fully understood, although dysfunction of this process contributes to the pathogenesis of multiple human retinal degenerative disorders, including age-related macular degeneration. Here, we present an integrated transcriptomic, proteomic, and phosphoproteomic analysis of phagocytosing RPE cells, utilizing three different experimental models: the human-derived RPE-like cell line ARPE-19, cultured murine primary RPE cells, and RPE samples from live mice. Our combined results indicated that early stages of phagocytosis in the RPE are mainly characterized by pronounced changes in the protein phosphorylation level. Global phosphoprotein enrichment analysis revealed involvement of PI3K/Akt, mechanistic target of rapamycin (mTOR), and MEK/ERK pathways in the regulation of RPE phagocytosis, confirmed by immunoblot analyses and in vitro phagocytosis assays. Most strikingly, phagocytosis of POS by cultured RPE cells was almost completely blocked by pharmacological inhibition of phosphorylation of Akt. Our findings, along with those of previous studies, indicate that these phosphorylation events allow the RPE to integrate multiple signals instigated by shed POS at different stages of the phagocytic process.
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Affiliation(s)
- Cheng-Kang Chiang
- From the Ottawa Institute of Systems Biology and Department of Biochemistry, Microbiology and Immunology, Faculty of Medicine, University of Ottawa, Ottawa, Ontario K1H 8M5, Canada.,the Department of Chemistry, National Dong Hwa University, No. 1 Sec. 2 Da Hsueh Road, Shoufeng, Hualien 97401, Taiwan
| | | | | | - Bo Xu
- From the Ottawa Institute of Systems Biology and Department of Biochemistry, Microbiology and Immunology, Faculty of Medicine, University of Ottawa, Ottawa, Ontario K1H 8M5, Canada
| | - Janice Mayne
- From the Ottawa Institute of Systems Biology and Department of Biochemistry, Microbiology and Immunology, Faculty of Medicine, University of Ottawa, Ottawa, Ontario K1H 8M5, Canada
| | - Zhibin Ning
- From the Ottawa Institute of Systems Biology and Department of Biochemistry, Microbiology and Immunology, Faculty of Medicine, University of Ottawa, Ottawa, Ontario K1H 8M5, Canada
| | - Daniel Figeys
- From the Ottawa Institute of Systems Biology and Department of Biochemistry, Microbiology and Immunology, Faculty of Medicine, University of Ottawa, Ottawa, Ontario K1H 8M5, Canada, .,the Canadian Institute for Advanced Research, Toronto, Ontario M5G 1Z8, Canada
| | - Krzysztof Palczewski
- the Department of Pharmacology and .,the Cleveland Center for Membrane and Structural Biology, School of Medicine, Case Western Reserve University, Cleveland, Ohio 44106, and
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Lakatos E, Stumpf MPH. Control mechanisms for stochastic biochemical systems via computation of reachable sets. ROYAL SOCIETY OPEN SCIENCE 2017; 4:160790. [PMID: 28878957 PMCID: PMC5579072 DOI: 10.1098/rsos.160790] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 05/15/2017] [Accepted: 07/21/2017] [Indexed: 06/07/2023]
Abstract
Controlling the behaviour of cells by rationally guiding molecular processes is an overarching aim of much of synthetic biology. Molecular processes, however, are notoriously noisy and frequently nonlinear. We present an approach to studying the impact of control measures on motifs of molecular interactions that addresses the problems faced in many biological systems: stochasticity, parameter uncertainty and nonlinearity. We show that our reachability analysis formalism can describe the potential behaviour of biological (naturally evolved as well as engineered) systems, and provides a set of bounds on their dynamics at the level of population statistics: for example, we can obtain the possible ranges of means and variances of mRNA and protein expression levels, even in the presence of uncertainty about model parameters.
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Affiliation(s)
- Eszter Lakatos
- Centre for Integrative Systems Biology and Bioinformatics, Department of Life Sciences, Biosciences, Imperial College London, London SW7 2AZ, UK
| | - Michael P. H. Stumpf
- Centre for Integrative Systems Biology and Bioinformatics, Department of Life Sciences, Biosciences, Imperial College London, London SW7 2AZ, UK
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Babtie AC, Stumpf MPH. How to deal with parameters for whole-cell modelling. J R Soc Interface 2017; 14:20170237. [PMID: 28768879 PMCID: PMC5582120 DOI: 10.1098/rsif.2017.0237] [Citation(s) in RCA: 52] [Impact Index Per Article: 7.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/30/2017] [Accepted: 06/22/2017] [Indexed: 11/12/2022] Open
Abstract
Dynamical systems describing whole cells are on the verge of becoming a reality. But as models of reality, they are only useful if we have realistic parameters for the molecular reaction rates and cell physiological processes. There is currently no suitable framework to reliably estimate hundreds, let alone thousands, of reaction rate parameters. Here, we map out the relative weaknesses and promises of different approaches aimed at redressing this issue. While suitable procedures for estimation or inference of the whole (vast) set of parameters will, in all likelihood, remain elusive, some hope can be drawn from the fact that much of the cellular behaviour may be explained in terms of smaller sets of parameters. Identifying such parameter sets and assessing their behaviour is now becoming possible even for very large systems of equations, and we expect such methods to become central tools in the development and analysis of whole-cell models.
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Affiliation(s)
- Ann C Babtie
- Department of Life Sciences, Imperial College London, London, UK
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Lenive O, W Kirk PD, H Stumpf MP. Inferring extrinsic noise from single-cell gene expression data using approximate Bayesian computation. BMC SYSTEMS BIOLOGY 2016; 10:81. [PMID: 27549182 PMCID: PMC4994381 DOI: 10.1186/s12918-016-0324-x] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 10/28/2015] [Accepted: 07/22/2016] [Indexed: 12/29/2022]
Abstract
Background Gene expression is known to be an intrinsically stochastic process which can involve single-digit numbers of mRNA molecules in a cell at any given time. The modelling of such processes calls for the use of exact stochastic simulation methods, most notably the Gillespie algorithm. However, this stochasticity, also termed “intrinsic noise”, does not account for all the variability between genetically identical cells growing in a homogeneous environment. Despite substantial experimental efforts, determining appropriate model parameters continues to be a challenge. Methods based on approximate Bayesian computation can be used to obtain posterior parameter distributions given the observed data. However, such inference procedures require large numbers of simulations of the model and exact stochastic simulation is computationally costly. In this work we focus on the specific case of trying to infer model parameters describing reaction rates and extrinsic noise on the basis of measurements of molecule numbers in individual cells at a given time point. Results To make the problem computationally tractable we develop an exact, model-specific, stochastic simulation algorithm for the commonly used two-state model of gene expression. This algorithm relies on certain assumptions and favourable properties of the model to forgo the simulation of the whole temporal trajectory of protein numbers in the system, instead returning only the number of protein and mRNA molecules present in the system at a specified time point. The computational gain is proportional to the number of protein molecules created in the system and becomes significant for systems involving hundreds or thousands of protein molecules. Conclusions We employ this simulation algorithm with approximate Bayesian computation to jointly infer the model’s rate and noise parameters from published gene expression data. Our analysis indicates that for most genes the extrinsic contributions to noise will be small to moderate but certainly are non-negligible. Electronic supplementary material The online version of this article (doi:10.1186/s12918-016-0324-x) contains supplementary material, which is available to authorized users.
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Affiliation(s)
| | - Paul D W Kirk
- MRC Biostatistics Unit, Cambridge Institute of Public Health, Cambridge, UK
| | - Michael P H Stumpf
- Imperial College, London, Centre for Integrative Systems Biology and Bioinformatics, London, SW7 2AZ, UK.
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