Abstract
Phase segregation of membranal components, such as proteins, lipids, and cholesterols, leads to the formation of aggregates or domains that are rich in specific constituents. This process is important in the interaction of the cell with its surroundings and in determining the cell's behavior and fate. Motivated by published experiments on curvature-modulated phase separation in lipid membranes, we formulate a mathematical model aiming at studying the spatial ordering of composition in a two-component biomembrane that is subjected to a prescribed (imposed) geometry. Based on this model, we identified key nondimensional quantities that govern the biomembrane response and performed numerical simulations to quantitatively explore their influence. We reproduce published experimental observations and extend them to surfaces with geometric features (imposed geometry) and lipid phases beyond those used in the experiments. In addition, we demonstrate the possibility for curvature-modulated phase separation above the critical temperature and propose a systematic procedure to determine which mechanism, the difference in bending stiffness or difference in spontaneous curvatures of the two phases, dominates the coupling between shape and composition.
Highlights
The biological lipid bilayer membrane, or in short “biomembrane,” is a fundamental building block of the cell
We formulated a simple mathematical model to study the spatial ordering of composition in a two-component biomembrane that is subjected to prescribed geometry
The mathematical model does not account for possible anisotropy of the membrane constituents or for possible interaction between lipids in the two leaflets of the bilayer membrane
Summary
The biological lipid bilayer membrane, or in short “biomembrane,” is a fundamental building block of the cell. Computational and Mathematical Methods in Medicine have generalized uniform composition models [24,25,26,27] to account for multicomponent or multiphase membranes [28,29,30,31,32,33,34,35] Features such as equilibrium configurations, stability [36,37,38,39], interaction with the cytoskeleton [40,41,42], formation of lipid rafts, anisotropy of the membrane constituents [43], and even using biomembranes as sensors or actuators [44, 45] have been investigated.
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