Stress field in actin gel growing on spherical substrate

Dafalias, YF; Pitouras, Z

dc.contributor.author	Dafalias, YF	en
dc.contributor.author	Pitouras, Z	en
dc.date.accessioned	2014-03-01T01:31:59Z
dc.date.available	2014-03-01T01:31:59Z
dc.date.issued	2009	en
dc.identifier.issn	1617-7959	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/20004
dc.subject.classification	Biophysics	en
dc.subject.classification	Engineering, Biomedical	en
dc.subject.other	Biomimetics	en
dc.subject.other	Chemical reactions	en
dc.subject.other	Cytology	en
dc.subject.other	Elasticity	en
dc.subject.other	Functional polymers	en
dc.subject.other	Gelation	en
dc.subject.other	Gels	en
dc.subject.other	Growth (materials)	en
dc.subject.other	Monomers	en
dc.subject.other	Poisson ratio	en
dc.subject.other	Polymerization	en
dc.subject.other	Polymers	en
dc.subject.other	Spheres	en
dc.subject.other	Strain	en
dc.subject.other	Actin filaments	en
dc.subject.other	Bio mimetic	en
dc.subject.other	Elastic materials	en
dc.subject.other	Finite straining	en
dc.subject.other	Gel growth	en
dc.subject.other	Gel medium	en
dc.subject.other	In-vitro	en
dc.subject.other	Latex beads	en
dc.subject.other	Mechanical coupling	en
dc.subject.other	Non-linear	en
dc.subject.other	Poisson	en
dc.subject.other	Radial directions	en
dc.subject.other	Small strains	en
dc.subject.other	Strain levels	en
dc.subject.other	Stress equilibrium	en
dc.subject.other	Stress fields	en
dc.subject.other	Stress variations	en
dc.subject.other	Unit vectors	en
dc.subject.other	Stresses	en
dc.subject.other	actin	en
dc.subject.other	molecular motor	en
dc.subject.other	article	en
dc.subject.other	binding site	en
dc.subject.other	chemical model	en
dc.subject.other	chemical structure	en
dc.subject.other	chemistry	en
dc.subject.other	computer simulation	en
dc.subject.other	crystallization	en
dc.subject.other	dimerization	en
dc.subject.other	gel	en
dc.subject.other	mechanical stress	en
dc.subject.other	methodology	en
dc.subject.other	protein binding	en
dc.subject.other	ultrastructure	en
dc.subject.other	young modulus	en
dc.subject.other	Actins	en
dc.subject.other	Binding Sites	en
dc.subject.other	Computer Simulation	en
dc.subject.other	Crystallization	en
dc.subject.other	Dimerization	en
dc.subject.other	Elastic Modulus	en
dc.subject.other	Gels	en
dc.subject.other	Models, Chemical	en
dc.subject.other	Models, Molecular	en
dc.subject.other	Molecular Motor Proteins	en
dc.subject.other	Protein Binding	en
dc.subject.other	Stress, Mechanical	en
dc.title	Stress field in actin gel growing on spherical substrate	en
heal.type	journalArticle	en
heal.identifier.primary	10.1007/s10237-007-0113-y	en
heal.identifier.secondary	http://dx.doi.org/10.1007/s10237-007-0113-y	en
heal.language	English	en
heal.publicationDate	2009	en
heal.abstract	Polymerization of actin to form an elastic gel is one of the main mechanisms responsible for cellular motility. The particular problem addressed here stems from the need to model theoretically the growth of actin gel under controlled conditions, as observed in experiments. A biomimetic in vitro system which consists of a spherical latex bead, coated by the enzymatic protein ActA, and a reconstituted cytoplasm within which such beads are placed, induces polymerization of actin on the surface of the bead in the form of successive elastic thin spherical layers. Each newly formed layer pushes outward, and is pushed inward by, the already formed spherical layers which altogether constitute an elastic spherical shell of thickness h varying with time. Thus, a stress field is created in the shell which in turn affects the rate of polymerization as well as that of dissociation of actin gel. Given this bio-chemo-mechanical coupling, the accurate determination of the stress field becomes a subject of great importance for the understanding of the process, and it is the main objective of this work. The problem is addressed by first assuming appropriate constitutive laws for the actin gel elastic material, and then solving the only non-trivial stress equilibrium differential equation along the radial direction assuming spherical symmetry. A linear and a non-linear constitutive model for isotropic elasticity is used, appropriate for small and finite strains, respectively, and the solution is found in closed analytical forms in both cases. Two important conclusions are reached. First, the stress field depends strongly on the compressibility of the actin gel medium via the value of the Poisson ratio, for both linear and non-linear analysis. Second, the linear and non-linear solutions are very close for small strains, but they diverge progressively as the strains increase from small to large. Guided by available experimental data on the observed strain levels, the analytical results are illustrated by selected graphs of stress variation along the radial direction. At the end some comments and suggestions on the bio-chemo-mechanical coupling of actin gel growth and resorption are presented, where the role of properly defined joint isotropic invariants of stress and a unit vector along the predominant direction of free ends of actin filaments at the polymerization site is introduced. © 2007 Springer-Verlag.	en
heal.publisher	SPRINGER HEIDELBERG	en
heal.journalName	Biomechanics and Modeling in Mechanobiology	en
dc.identifier.doi	10.1007/s10237-007-0113-y	en
dc.identifier.isi	ISI:000262532800002	en
dc.identifier.volume	8	en
dc.identifier.issue	1	en
dc.identifier.spage	9	en
dc.identifier.epage	24	en