Wang, Xiaoqiang; Du, Qiang Modelling and simulations of multi-component lipid membranes and open membranes via diffuse interface approaches. (English) Zbl 1143.92001 J. Math. Biol. 56, No. 3, 347-371 (2008). Summary: Diffuse interface (phase field) models are developed for multi-component vesicle membranes with different lipid compositions and membranes with free boundary. These models are used to simulate the deformation of membranes under the elastic bending energy and the line tension energy with prescribed volume and surface area constraints. By comparing our numerical simulations with recent biological experiments, it is demonstrated that the diffuse interface models can effectively capture the rich phenomena associated with the multi-component vesicle transformation and thus offering great functionality in their simulation and modelling. Cited in 72 Documents MSC: 92C05 Biophysics 65C20 Probabilistic models, generic numerical methods in probability and statistics 92C10 Biomechanics 92-08 Computational methods for problems pertaining to biology Keywords:vesicle membrane; lipid bilayer; multi-component membrane; open membrane; phase field model; diffuse interface model; numerical simulation; Gaussian curvature energy Software:PHENIX; MATCONT; Schittkowski PDFBibTeX XMLCite \textit{X. Wang} and \textit{Q. Du}, J. Math. Biol. 56, No. 3, 347--371 (2008; Zbl 1143.92001) Full Text: DOI arXiv References: [1] Anderson D., McFadden G., Wheeler A. (1998). Diffuse-interface methods in fluid mechanisms. Annu. Rev. Fluid Mech. 30: 139–165 · Zbl 1398.76051 [2] Baumgart T., Das S., Webb W., Jenkins J. (2005). Membrane elasticity in giant vesicles with fluid phase coexistence. Biophys. J. 89: 1067–1080 [3] Baumgart T., Hess S., Webb W. (2003). Imaging coexisting fluid domains in biomembrane models coupling curvature and line tension. 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