On the asymptotic regime of a model for friction mediated by transient elastic linkages

Milisic, Vuk and Oelz, Dietmar (2011) On the asymptotic regime of a model for friction mediated by transient elastic linkages. Journal de Mathematiques Pures et Appliquees, 96 5: 484-501. doi:10.1016/j.matpur.2011.03.005

Author Milisic, Vuk
Oelz, Dietmar
Title On the asymptotic regime of a model for friction mediated by transient elastic linkages
Journal name Journal de Mathematiques Pures et Appliquees   Check publisher's open access policy
ISSN 0021-7824
Publication date 2011-11-01
Sub-type Article (original research)
DOI 10.1016/j.matpur.2011.03.005
Open Access Status Not yet assessed
Volume 96
Issue 5
Start page 484
End page 501
Total pages 18
Place of publication Issy les Moulineaux, France
Publisher Elsevier Masson
Language eng
Abstract In this work we study a system of an integral equation of Volterra type coupled with an original renewal equation. This model arises in the context of cell motility (Oelz et al., 2008 [6]): the integral equation describes the trajectory of a binding site which is connected via transiently remodelling linkages to the substrate and which evolves driven by a given force. The renewal model accounts for the remodelling process of linkages which attach and break with given probabilities. In the present paper we analyze existence and uniqueness issues for the coupled system of interest and provide a rigorous justification of the asymptotic limit of infinitesimally rapid turnover of linkages. The renewal model for the age distribution of linkages differs from more classical ones in that it describes competition between population size and birth and because it admits a new and specific Lyapunov functional. On the other side, using a comparison principle which applies to non-convolution linear Volterra kernels and the peculiar transport properties of the linkages, one establishes a convergence result when the turnover parameter ε tends to zero.
Keyword Friction coefficient
Protein linkages
Cell adhesion
Renewal equation
Effect of chemical bonds
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Non-UQ

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Mathematics and Physics
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Created: Sat, 14 Jan 2017, 02:15:26 EST by Kay Mackie on behalf of School of Mathematics & Physics