title: A continuous mechanobiological model of lateral inhomogeneous biological surfaces
creator: Mercker, Moritz
creator: Marciniak-Czochra, Anna
creator: Hartmann, Dirk
subject: ddc-510
subject: 510 Mathematics
description: Thin elastic surfaces containing molecules infuencing the mechanical prop-  erties of the surface itself are wide spreaded structures of different scales in  biological systems. Prominent examples are bilayer membranes and cell tis-  sues. In this paper we present a continuous dynamical model of deforming  lateral inhomogeneous surfaces, using the example of biological membranes.  In agreement with experimental observations the membrane consists of dif-  ferent molecule species undergoing lateral phase separation and influencing  the mechanical properties of the membrane. The presented model is based on  the minimization of a free energy leading to a coupled nonlinear PDE system  of fourth order, related to the Willmore flow and the Cahn-Hilliard equation.  First simulations show the development of budding structures from stochas-  tic initial conditions as a result of the gradient flow, which is comparable  to experimentally observed structures. In our model mechanical properties  are described via macroscopic mechanical moduli. However, the qualitative  and quantitative relationships of mechanical moduli and the local composi-  tion of the membrane are unkown. Since the exact relationship significantly  influences the emerging structures, this study motivates the development of  techniques allowing for upscaling from the molecular scale. 
date: 2011
type: Preprint
type: info:eu-repo/semantics/preprint
type: NonPeerReviewed
format: application/pdf
identifier: https://archiv.ub.uni-heidelberg.de/volltextserverhttps://archiv.ub.uni-heidelberg.de/volltextserver/11591/1/preprint_mercker.pdf
identifier: DOI:10.11588/heidok.00011591
identifier: urn:nbn:de:bsz:16-opus-115916
identifier:   Mercker, Moritz ; Marciniak-Czochra, Anna ; Hartmann, Dirk  (2011) A continuous mechanobiological model of lateral inhomogeneous biological surfaces.  [Preprint]     
relation: https://archiv.ub.uni-heidelberg.de/volltextserver/11591/
rights: info:eu-repo/semantics/openAccess
rights: http://archiv.ub.uni-heidelberg.de/volltextserver/help/license_urhg.html
language: eng