Mechanics of lipid bilayer junctions affecting the size of a connecting lipid nanotube

In this study we report a physical analysis of the membrane mechanics affecting the size of the highly curved region of a lipid nanotube (LNT) that is either connected between a lipid bilayer vesicle and the tip of a glass microinjection pipette (tube-only) or between a lipid bilayer vesicle and a vesicle that is attached to the tip of a glass microinjection pipette (two-vesicle). For the tube-only configuration (TOC), a micropipette is used to pull a LNT into the interior of a surface-immobilized vesicle, where the length of the tube L is determined by the distance of the micropipette to the vesicle wall. For the two-vesicle configuration (TVC), a small vesicle is inflated at the tip of the micropipette tip and the length of the tube L is in this case determined by the distance between the two interconnected vesicles. An electrochemical method monitoring diffusion of electroactive molecules through the nanotube has been used to determine the radius of the nanotube R as a function of nanotube length L for the two configurations. The data show that the LNT connected in the TVC constricts to a smaller radius in comparison to the tube-only mode and that tube radius shrinks at shorter tube lengths. To explain these electrochemical data, we developed a theoretical model taking into account the free energy of the membrane regions of the vesicles, the LNT and the high curvature junctions. In particular, this model allows us to estimate the surface tension coefficients from R(L) measurements

Numerics of boundary-domain integral and integro-differential equations for BVP with variable coefficient in 3D

This is the post-print version of the article. The official published version can be accessed from the links below - Copyright @ 2013 Springer-VerlagA numerical implementation of the direct boundary-domain integral and integro-differential equations, BDIDEs, for treatment of the Dirichlet problem for a scalar elliptic PDE with variable coefficient in a three-dimensional domain is discussed. The mesh-based discretisation of the BDIEs with tetrahedron domain elements in conjunction with collocation method leads to a system of linear algebraic equations (discretised BDIE). The involved fully populated matrices are approximated by means of the H-Matrix/adaptive cross approximation technique. Convergence of the method is investigated.This study is partially supported by the EPSRC grant EP/H020497/1:"Mathematical Analysis of Localised-Boundary-Domain Integral Equations for Variable-Coefficients Boundary Value Problems"

A convolution thresholding scheme for the Willmore flow

A convolution thresholding scheme fro geometric Willmore flows is suggested and the consistency is proved

A convolution-thresholding approximation of generalized curvature flows

We construct a convolution-thresholding approximation scheme for the geometric surface evolution in the case when the velocity of the surface at each point is a given function of the mean curvature. Conditions for the monotonicity of the scheme are found and the convergence of the approximations to the corresponding viscosity solution is proved. We also discuss some aspects of the numerical implementation of such schemes and present several numerical results