The indentation of pressurized elastic shells: from polymeric capsules to yeast cells

Handle URI:
http://hdl.handle.net/10754/599919
Title:
The indentation of pressurized elastic shells: from polymeric capsules to yeast cells
Authors:
Vella, D.; Ajdari, A.; Vaziri, A.; Boudaoud, A.
Abstract:
Pressurized elastic capsules arise at scales ranging from the 10 m diameter pressure vessels used to store propane at oil refineries to the microscopic polymeric capsules that may be used in drug delivery. Nature also makes extensive use of pressurized elastic capsules: plant cells, bacteria and fungi have stiff walls, which are subject to an internal turgor pressure. Here, we present theoretical, numerical and experimental investigations of the indentation of a linearly elastic shell subject to a constant internal pressure. We show that, unlike unpressurized shells, the relationship between force and displacement demonstrates two linear regimes. We determine analytical expressions for the effective stiffness in each of these regimes in terms of the material properties of the shell and the pressure difference. As a consequence, a single indentation experiment over a range of displacements may be used as a simple assay to determine both the internal pressure and elastic properties of capsules. Our results are relevant for determining the internal pressure in bacterial, fungal or plant cells. As an illustration of this, we apply our results to recent measurements of the stiffness of baker's yeast and infer from these experiments that the internal osmotic pressure of yeast cells may be regulated in response to changes in the osmotic pressure of the external medium.
Citation:
Vella D, Ajdari A, Vaziri A, Boudaoud A (2011) The indentation of pressurized elastic shells: from polymeric capsules to yeast cells. Journal of The Royal Society Interface 9: 448–455. Available: http://dx.doi.org/10.1098/rsif.2011.0352.
Publisher:
The Royal Society
Journal:
Journal of The Royal Society Interface
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
10-Aug-2011
DOI:
10.1098/rsif.2011.0352
PubMed ID:
21831894
PubMed Central ID:
PMC3262421
Type:
Article
ISSN:
1742-5689; 1742-5662
Sponsors:
D.V. was supported by an Oppenheimer Early Career Fellowship. This publication is based on work supported in part by Award no. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST). A. A. and A. V. are thankful for the support of NSF CMMI grant award no. 1065759. A. B. was supported by ANR-BLANC-Mechastem. We are grateful to Mark Hallworth and Sebastien Moulinet for their assistance with the experimental aspects, and to Mokhtar Adda-Bedia for encouragement and for laboratory space.
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Full metadata record

DC FieldValue Language
dc.contributor.authorVella, D.en
dc.contributor.authorAjdari, A.en
dc.contributor.authorVaziri, A.en
dc.contributor.authorBoudaoud, A.en
dc.date.accessioned2016-02-28T06:32:26Zen
dc.date.available2016-02-28T06:32:26Zen
dc.date.issued2011-08-10en
dc.identifier.citationVella D, Ajdari A, Vaziri A, Boudaoud A (2011) The indentation of pressurized elastic shells: from polymeric capsules to yeast cells. Journal of The Royal Society Interface 9: 448–455. Available: http://dx.doi.org/10.1098/rsif.2011.0352.en
dc.identifier.issn1742-5689en
dc.identifier.issn1742-5662en
dc.identifier.pmid21831894en
dc.identifier.doi10.1098/rsif.2011.0352en
dc.identifier.urihttp://hdl.handle.net/10754/599919en
dc.description.abstractPressurized elastic capsules arise at scales ranging from the 10 m diameter pressure vessels used to store propane at oil refineries to the microscopic polymeric capsules that may be used in drug delivery. Nature also makes extensive use of pressurized elastic capsules: plant cells, bacteria and fungi have stiff walls, which are subject to an internal turgor pressure. Here, we present theoretical, numerical and experimental investigations of the indentation of a linearly elastic shell subject to a constant internal pressure. We show that, unlike unpressurized shells, the relationship between force and displacement demonstrates two linear regimes. We determine analytical expressions for the effective stiffness in each of these regimes in terms of the material properties of the shell and the pressure difference. As a consequence, a single indentation experiment over a range of displacements may be used as a simple assay to determine both the internal pressure and elastic properties of capsules. Our results are relevant for determining the internal pressure in bacterial, fungal or plant cells. As an illustration of this, we apply our results to recent measurements of the stiffness of baker's yeast and infer from these experiments that the internal osmotic pressure of yeast cells may be regulated in response to changes in the osmotic pressure of the external medium.en
dc.description.sponsorshipD.V. was supported by an Oppenheimer Early Career Fellowship. This publication is based on work supported in part by Award no. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST). A. A. and A. V. are thankful for the support of NSF CMMI grant award no. 1065759. A. B. was supported by ANR-BLANC-Mechastem. We are grateful to Mark Hallworth and Sebastien Moulinet for their assistance with the experimental aspects, and to Mokhtar Adda-Bedia for encouragement and for laboratory space.en
dc.publisherThe Royal Societyen
dc.subjectBucklingen
dc.subjectCell wallen
dc.subjectFinite-element methoden
dc.subjectTurgor regulationen
dc.subject.meshCellsen
dc.subject.meshCapsulesen
dc.subject.meshFinite Element Analysisen
dc.subject.meshElasticityen
dc.subject.meshPressureen
dc.subject.meshModels, Theoreticalen
dc.titleThe indentation of pressurized elastic shells: from polymeric capsules to yeast cellsen
dc.typeArticleen
dc.identifier.journalJournal of The Royal Society Interfaceen
dc.identifier.pmcidPMC3262421en
dc.contributor.institutionUniversity of Cambridge, Cambridge, United Kingdomen
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
dc.contributor.institutionNortheastern University, Boston, United Statesen
dc.contributor.institutionUniversite de Lyon, Lyon, Franceen
kaust.grant.numberKUK-C1-013-04en

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