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      The circadian clock of the bacterium B. subtilis evokes properties of complex, multicellular circadian systems

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          Abstract

          Circadian clocks are pervasive throughout nature, yet only recently has this adaptive regulatory program been described in nonphotosynthetic bacteria. Here, we describe an inherent complexity in the Bacillus subtilis circadian clock. We find that B. subtilis entrains to blue and red light and that circadian entrainment is separable from masking through fluence titration and frequency demultiplication protocols. We identify circadian rhythmicity in constant light, consistent with the Aschoff’s rule, and entrainment aftereffects, both of which are properties described for eukaryotic circadian clocks. We report that circadian rhythms occur in wild isolates of this prokaryote, thus establishing them as a general property of this species, and that its circadian system responds to the environment in a complex fashion that is consistent with multicellular eukaryotic circadian systems.

          Abstract

          Characteristics of complex circadian organization are exemplified in a non-photosynthetic prokaryote.

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          Fitting Linear Mixed-Effects Models Usinglme4

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              Fitting Linear Mixed-Effects Models Using lme4

              Maximum likelihood or restricted maximum likelihood (REML) estimates of the parameters in linear mixed-effects models can be determined using the lmer function in the lme4 package for R. As for most model-fitting functions in R, the model is described in an lmer call by a formula, in this case including both fixed- and random-effects terms. The formula and data together determine a numerical representation of the model from which the profiled deviance or the profiled REML criterion can be evaluated as a function of some of the model parameters. The appropriate criterion is optimized, using one of the constrained optimization functions in R, to provide the parameter estimates. We describe the structure of the model, the steps in evaluating the profiled deviance or REML criterion, and the structure of classes or types that represents such a model. Sufficient detail is included to allow specialization of these structures by users who wish to write functions to fit specialized linear mixed models, such as models incorporating pedigrees or smoothing splines, that are not easily expressible in the formula language used by lmer. Journal of Statistical Software, 67 (1) ISSN:1548-7660
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                Author and article information

                Contributors
                Role: ConceptualizationRole: Data curationRole: Formal analysisRole: Funding acquisitionRole: InvestigationRole: MethodologyRole: Project administrationRole: ValidationRole: VisualizationRole: Writing - original draftRole: Writing - review & editing
                Role: Data curationRole: ResourcesRole: Writing - review & editing
                Role: InvestigationRole: MethodologyRole: Validation
                Role: ConceptualizationRole: Formal analysisRole: Funding acquisitionRole: MethodologyRole: Project administrationRole: VisualizationRole: Writing - original draftRole: Writing - review & editing
                Role: ConceptualizationRole: MethodologyRole: ResourcesRole: Supervision
                Role: ConceptualizationRole: Funding acquisitionRole: MethodologyRole: Project administrationRole: ResourcesRole: SupervisionRole: ValidationRole: VisualizationRole: Writing - original draftRole: Writing - review & editing
                Journal
                Sci Adv
                Sci Adv
                sciadv
                advances
                Science Advances
                American Association for the Advancement of Science
                2375-2548
                August 2023
                04 August 2023
                : 9
                : 31
                : eadh1308
                Affiliations
                [ 1 ]Institute of Medical Psychology, Medical Faculty, LMU Munich, Munich, Germany.
                [ 2 ]Bacterial Interactions and Evolution Group, DTU Bioengineering, Technical University of Denmark, Kongens Lyngby, Denmark.
                [ 3 ]Institute of Biology Leiden, Leiden University, Leiden, Netherlands.
                [ 4 ]Department of Cell and Developmental Biology, John Innes Centre, Norwich Research Park, Norwich, UK.
                Author notes
                [* ]Corresponding author. Email: francesca.sartor@ 123456med.uni-muenchen.de (F.S.); merrow@ 123456lmu.de (M.M.)
                Author information
                https://orcid.org/0000-0002-2898-3833
                https://orcid.org/0000-0002-3203-4526
                https://orcid.org/0000-0001-6859-0105
                https://orcid.org/0000-0002-4465-1636
                https://orcid.org/0000-0002-8688-2360
                Article
                adh1308
                10.1126/sciadv.adh1308
                10403212
                37540742
                8e4d3b6f-cb82-4fa0-b837-b32d5696de89
                Copyright © 2023 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works. Distributed under a Creative Commons Attribution License 4.0 (CC BY).

                This is an open-access article distributed under the terms of the Creative Commons Attribution license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

                History
                : 12 February 2023
                : 05 July 2023
                Funding
                Funded by: FundRef http://dx.doi.org/10.13039/501100000268, Biotechnology and Biological Sciences Research Council;
                Award ID: BB/P013511/1
                Funded by: FundRef http://dx.doi.org/10.13039/501100000268, Biotechnology and Biological Sciences Research Council;
                Award ID: BB/X01102X/1
                Funded by: FundRef http://dx.doi.org/10.13039/501100001659, Deutsche Forschungsgemeinschaft;
                Award ID: 507872050
                Funded by: Chinese Scholarship Council fellowship;
                Funded by: Volkswagen Foundation (Life? Funding Program: “The Fourth Dimension E;
                Funded by: Friedrich Bauer Stiftung;
                Funded by: Verein zur Förderung von Wissenschaft und Forschung of the LMU Munich;
                Categories
                Research Article
                Biomedicine and Life Sciences
                SciAdv r-articles
                Microbiology
                Microbiology
                Custom metadata
                SEF RIO

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