Geometric evolution towards the understanding of biomembranes
Final Report Abstract
Biological membranes are a mixture of many different types of lipids and protein components, and their relative amount and composition differ between functionally distinct domains. The strongly increasing interest in lipid membranes results from the hypothesized coupling of lipid phase segregation in the membrane to fundamental cell biological processes, such as membrane signaling and trafficing. With the curvature as one of the crucial ingredients to determine properties of membranes it seems natural to model the evolution within a continuum framework. Within this project, thermodynamically consistent models for the coupling of membrane morphology and composition of lipids and proteins are derived and numerically analyzed. 3D simulations are based on phase field approximations along the membrane, combined with a parametric finite element approach for the membrane evolution, or a fully implicit description of composition and morphology within a phase field framework. In the latter case, we have mainly focused on bulk fluid interactions, using Stokes and Navier-Stokes equations, consider numerical approaches to fulfill local inextensibility constraints for the membrane and model the influence of proteins on the membrane. The derived models and algorithms are used to answer questions, related to tumbling instabilities in shear flow, fluid-structure interactions on clustered stereocilia, coarsening of lipid domains under the influence of protein inclusions and surface viscosity. All simulations are done within the parallel adaptive finite element toolbox AMDiS.
Publications
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AMDiS - adaptive multidimensional simulations. Comput. Vis. Sci., 10 (2007), 57-66
S. Vey, A. Voigt
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Dynamics of multicomponent vesicles in a viscous fluid. J. Comput. Phys., 229 (1) (2010), 119-144
J. S. Sohn, Y.-H. Tseng, Sh. Li, A. Voigt, J. S. Lowengrub
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Forces between clustered stereocilia minimize friction in the ear on a subnanometre scale. Nature, 474 (2011), 376-379
A. S. Kozlov, J. Baumgart, T. Risler, C. P. C. Versteegh, A. J. Hudspeth
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A finite element approach to incompressible two-phase flow on manifolds. J. Fluid Mech., 708 (2012), 418-438
I. Nitschke, A. Voigt, J. Wensch
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The influence of membrane bound proteins on phase separation and coarsening in cell membranes. Phys. Chem. Chem. Phys., 14 (2012), 14509-14515
T. Witkowski, R. Backofen, A. Voigt
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Diffuse interface models of locally inextensible vesicles in a viscous fluid. Journal of Computational Physics, Volume 277, 15 November 2014, Pages 32-47
S. Aland, S. Egerer, J. Lowengrub, A. Voigt
