Continuum Modeling of Bilayer Lipid Membranes
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0924-Z08-03
Continuum Modeling of Bilayer Lipid Membranes Raffaella De Vita, David Hopkinson, Vishnu B. Sundaresan, and Donald J. Leo Mechanical Engineering, Virginia Tech, 310 Durham Hall, Blacksburg, Virginia, 24061
ABSTRACT A continuum model is used for the description of the mechanical response of bilayer lipid membranes (BLMs) subjected to hydrostatic pressure. The model is formulated under the assumption that the BLMs are Smectic A liquid crystals. The mean orientation of the amphiphilic molecules is postulated to be perpendicular to the lipid layers and each layer is idealized as a two dimensional liquid. The permeation process governs the motion of the molecules through the smectic layers. The approach taken in this study is based on the seminal works of Helfrich [1] and de Gennes [2] on Smectic A liquid crystals. The failure process of the BLMs, which is observed in the experimental studies, is considered to be due to extrusion of the BLMs through the pores of the polycarbonate filters. INTRODUCTION Lipid bilayer assemblies have demonstrated their potential use in many applications ranging from drug delivery systems to biosensors for detecting biological agents. At CIMSS (Center for Intelligent Material Systems and Structures), Virginia Tech, the biological principles of BLMs are being exploited to develop a new generation of smart materials, the so-called nastic materials [3]. Like plants, these materials are envisioned to generate high strains and stresses in response to enviromental stimulations. Despite the growing interest in lipid bilayers for medical, defense, and engineering applications [4, 5, 6], a rigorous characterization of their mechanical properties remains limited due to their peculiar structure, nanometer size thickness, and poor stability. The lipid bilayers possess mechanical properties that are intermediate between those of crystalline solids and amorphous liquids: although the molecules are free to move, they preserve some orientational order. Moreover, they are 5nm thick and unstable to environmental disturbances. Because of the complex structure of lipid bilayers, experimental investigations of their material properties remain difficult. Thus, the formulation of reliable mathematical models becomes important in gaining a superior understanding of the mechanical characteristics of these bio-membranes. Continuum models, which are currently used to interpret the results of experimental studies, are based on the simplifying assumption that the lipid bilayers behave as solids or fluids. These models include linear elastic and viscoelastic solid models, Newtonian, Maxwell, and shear thinning liquid drop models. However, lipid bilayers have been universally recognized to be Smectic A lyotropic liquid crystals [2, 7]. Thus, the continuum models that help in interpreting the experimental studies need to be formulated under the more physically reasonable assumption that the lipid bilayers are Smectic-A liquid crystals. In this study, the continuum theory of liquid crystals developed by Helfri
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