title: The indentation of pressurized elastic shells: from polymeric capsules to yeast cells.
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.
authors.affiliation: Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK. dominic.vella@maths.ox.ac.uk
authors.forename: Dominic
authors.initials: D
authors.lastname: Vella
authors.forename: Amin
authors.initials: A
authors.lastname: Ajdari
authors.forename: Ashkan
authors.initials: A
authors.lastname: Vaziri
authors.forename: Arezki
authors.initials: A
authors.lastname: Boudaoud
mesh_terms: D001703:Biophysics; D002214:Capsules; D002477:Cells; D004548:Elasticity; D020342:Finite Element Analysis; D008422:Materials Testing / Q000379:methods*; D008962:Models, Theoretical; D011312:Pressure
chemical_list: D002214:Capsules