Bistable emergence of oscillations in growing Bacillus subtilis biofilms

Biofilm communities of Bacillus subtilis bacteria have recently been shown to exhibit collective growth-rate oscillations mediated by electrochemical signaling to cope with nutrient starvation. These oscillations emerge once the colony reaches a large enough number of cells. However, it remains uncl...

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Detalles Bibliográficos
Autores: Martínez Corral, Rosa, 1991-, Liu, Jintao, Süel, Gürol M., García Ojalvo, Jordi
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2018
País:España
Institución:Universitat Pompeu Fabra
Repositorio:Repositorio Digital de la UPF
OAI Identifier:oai:repositori.upf.edu:10230/41990
Acceso en línea:http://hdl.handle.net/10230/41990
http://dx.doi.org/10.1073/pnas.1805004115
Access Level:acceso abierto
Palabra clave:Biofilm growth
Biological oscillations
Delay-induced oscillations
Delayed negative feedback
Subcritical Hopf bifurcation
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spelling Bistable emergence of oscillations in growing Bacillus subtilis biofilmsMartínez Corral, Rosa, 1991-Liu, JintaoSüel, Gürol M.García Ojalvo, JordiBiofilm growthBiological oscillationsDelay-induced oscillationsDelayed negative feedbackSubcritical Hopf bifurcationBiofilm communities of Bacillus subtilis bacteria have recently been shown to exhibit collective growth-rate oscillations mediated by electrochemical signaling to cope with nutrient starvation. These oscillations emerge once the colony reaches a large enough number of cells. However, it remains unclear whether the amplitude of the oscillations, and thus their effectiveness, builds up over time gradually or if they can emerge instantly with a nonzero amplitude. Here we address this question by combining microfluidics-based time-lapse microscopy experiments with a minimal theoretical description of the system in the form of a delay-differential equation model. Analytical and numerical methods reveal that oscillations arise through a subcritical Hopf bifurcation, which enables instant high-amplitude oscillations. Consequently, the model predicts a bistable regime where an oscillating and a nonoscillating attractor coexist in phase space. We experimentally validate this prediction by showing that oscillations can be triggered by perturbing the media conditions, provided the biofilm size lies within an appropriate range. The model also predicts that the minimum size at which oscillations start decreases with stress, a fact that we also verify experimentally. Taken together, our results show that collective oscillations in cell populations can emerge suddenly with nonzero amplitude via a discontinuous transition.This work was supported by the Spanish Ministry of Economy and Competitiveness and Fondo Europeo de Desarrollo Regional (Project FIS2015-66503-C3-1-P) and by the Generalitat de Catalunya (Project 2017 SGR 1054). R.M.-C. acknowledges financial support from La Caixa Foundation. J.G.-O. acknowledges support from the Institució Catalana de Recerca i Estudis Avançats Academia programme and from the “María de Maeztu” Programme for Units of Excellence in Research and Development (Spanish Ministry of Economy and Competitiveness, MDM-2014-0370). J.L. acknowledges support from the J.L. acknowledges support from the Tsinghua–Peking Center for Life Sciences and the Thousand Talents Program of China. G.M.S. acknowledges support for this research from the San Diego Center for Systems Biology (NIH Grant P50 GM085764), the National Institute of General Medical Sciences (Grant R01 GM121888 to G.M.S.), the Defense Advanced Research Projects Agency (Grant HR0011-16-2-0035 to G.M.S.), and the Howard Hughes Medical Institute–Simons Foundation Faculty Scholars program (G.M.S.).National Academy of Sciences201920192018info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfapplication/pdfhttp://hdl.handle.net/10230/41990http://dx.doi.org/10.1073/pnas.1805004115reponame:Repositorio Digital de la UPFinstname:Universitat Pompeu FabraInglésProceedings of the National Academy of Sciences of the United States of America. 2018;115(36):8333-40info:eu-repo/grantAgreement/ES/1PE/FIS2015-66503-C3-1-P© National Academy of Sciencesinfo:eu-repo/semantics/openAccessoai:repositori.upf.edu:10230/419902026-06-12T07:21:37Z
dc.title.none.fl_str_mv Bistable emergence of oscillations in growing Bacillus subtilis biofilms
title Bistable emergence of oscillations in growing Bacillus subtilis biofilms
spellingShingle Bistable emergence of oscillations in growing Bacillus subtilis biofilms
Martínez Corral, Rosa, 1991-
Biofilm growth
Biological oscillations
Delay-induced oscillations
Delayed negative feedback
Subcritical Hopf bifurcation
title_short Bistable emergence of oscillations in growing Bacillus subtilis biofilms
title_full Bistable emergence of oscillations in growing Bacillus subtilis biofilms
title_fullStr Bistable emergence of oscillations in growing Bacillus subtilis biofilms
title_full_unstemmed Bistable emergence of oscillations in growing Bacillus subtilis biofilms
title_sort Bistable emergence of oscillations in growing Bacillus subtilis biofilms
dc.creator.none.fl_str_mv Martínez Corral, Rosa, 1991-
Liu, Jintao
Süel, Gürol M.
García Ojalvo, Jordi
author Martínez Corral, Rosa, 1991-
author_facet Martínez Corral, Rosa, 1991-
Liu, Jintao
Süel, Gürol M.
García Ojalvo, Jordi
author_role author
author2 Liu, Jintao
Süel, Gürol M.
García Ojalvo, Jordi
author2_role author
author
author
dc.subject.none.fl_str_mv Biofilm growth
Biological oscillations
Delay-induced oscillations
Delayed negative feedback
Subcritical Hopf bifurcation
topic Biofilm growth
Biological oscillations
Delay-induced oscillations
Delayed negative feedback
Subcritical Hopf bifurcation
description Biofilm communities of Bacillus subtilis bacteria have recently been shown to exhibit collective growth-rate oscillations mediated by electrochemical signaling to cope with nutrient starvation. These oscillations emerge once the colony reaches a large enough number of cells. However, it remains unclear whether the amplitude of the oscillations, and thus their effectiveness, builds up over time gradually or if they can emerge instantly with a nonzero amplitude. Here we address this question by combining microfluidics-based time-lapse microscopy experiments with a minimal theoretical description of the system in the form of a delay-differential equation model. Analytical and numerical methods reveal that oscillations arise through a subcritical Hopf bifurcation, which enables instant high-amplitude oscillations. Consequently, the model predicts a bistable regime where an oscillating and a nonoscillating attractor coexist in phase space. We experimentally validate this prediction by showing that oscillations can be triggered by perturbing the media conditions, provided the biofilm size lies within an appropriate range. The model also predicts that the minimum size at which oscillations start decreases with stress, a fact that we also verify experimentally. Taken together, our results show that collective oscillations in cell populations can emerge suddenly with nonzero amplitude via a discontinuous transition.
publishDate 2018
dc.date.none.fl_str_mv 2018
2019
2019
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/10230/41990
http://dx.doi.org/10.1073/pnas.1805004115
url http://hdl.handle.net/10230/41990
http://dx.doi.org/10.1073/pnas.1805004115
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Proceedings of the National Academy of Sciences of the United States of America. 2018;115(36):8333-40
info:eu-repo/grantAgreement/ES/1PE/FIS2015-66503-C3-1-P
dc.rights.none.fl_str_mv © National Academy of Sciences
info:eu-repo/semantics/openAccess
rights_invalid_str_mv © National Academy of Sciences
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv National Academy of Sciences
publisher.none.fl_str_mv National Academy of Sciences
dc.source.none.fl_str_mv reponame:Repositorio Digital de la UPF
instname:Universitat Pompeu Fabra
instname_str Universitat Pompeu Fabra
reponame_str Repositorio Digital de la UPF
collection Repositorio Digital de la UPF
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repository.mail.fl_str_mv
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