Equilibrium Theory and Geometrical Constraint Equation for Two-Component Lipid Bilayer Vesicles |
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Authors: | Yajun Yin Cunjing Lv |
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Institution: | (1) Department of Engineering Mechanics, School of Aerospace, FML, Tsinghua University, 100084 Beijing, China |
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Abstract: | This paper aims at the general mathematical framework for the equilibrium theory of two-component lipid bilayer vesicles.
To take into account the influences of the local compositions together with the mean curvature and Gaussian curvature of the
membrane surface, a general potential functional is constructed. We introduce two kinds of virtual displacement modes: the
normal one and the tangential one. By minimizing the potential functional, the equilibrium differential equations and the
boundary conditions of two-component lipid vesicles are derived. Additionally, the geometrical constraint equation and geometrically
permissible condition for the two-component lipid vesicles are presented. The physical, mathematical, and biological meanings
of the equilibrium differential equations and the geometrical constraint equations are discussed. The influences of physical
parameters on the geometrically permissible phase diagrams are predicted. Numerical results can be used to explain recent
experiments. |
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Keywords: | Two-component Lipid bilayer Geometrical constraint equation Differential operators Arbitrary virtual displacement mode |
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