Article
Shape and stability of twodimensional lipid domains with dipoledipole interactions
Department of Physical Electronics, Tokyo Institute of Technology, Meguroku, Tokyo 1528552, Japan.
The Journal of Chemical Physics (Impact Factor: 2.95). 01/2007; 125(22):224701. DOI: 10.1063/1.2402160 Source: PubMed
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 "where N is the normal vector at x and H is the mean curvature. Highorder curvatures have been extensively studied in the context of membrane bending analysis (Canham, 1970; Helfrich, 1973; OuYang and Helfrich, 1989; Iwamoto et al., 2006). "
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ABSTRACT: Large chemical and biological systems such as fuel cells, ion channels, molecular motors, and viruses are of great importance to the scientific community and public health. Typically, these complex systems in conjunction with their aquatic environment pose a fabulous challenge to theoretical description, simulation, and prediction. In this work, we propose a differential geometry based multiscale paradigm to model complex macromolecular systems, and to put macroscopic and microscopic descriptions on an equal footing. In our approach, the differential geometry theory of surfaces and geometric measure theory are employed as a natural means to couple the macroscopic continuum mechanical description of the aquatic environment with the microscopic discrete atomistic description of the macromolecule. Multiscale free energy functionals, or multiscale action functionals are constructed as a unified framework to derive the governing equations for the dynamics of different scales and different descriptions. Two types of aqueous macromolecular complexes, ones that are near equilibrium and others that are far from equilibrium, are considered in our formulations. We show that generalized NavierStokes equations for the fluid dynamics, generalized Poisson equations or generalized PoissonBoltzmann equations for electrostatic interactions, and Newton's equation for the molecular dynamics can be derived by the least action principle. These equations are coupled through the continuumdiscrete interface whose dynamics is governed by potential driven geometric flows. Comparison is given to classical descriptions of the fluid and electrostatic interactions without geometric flow based micromacro interfaces. The detailed balance of forces is emphasized in the present work. We further extend the proposed multiscale paradigm to micromacro analysis of electrohydrodynamics, electrophoresis, fuel cells, and ion channels. We derive generalized PoissonNernstPlanck equations that are coupled to generalized NavierStokes equations for fluid dynamics, Newton's equation for molecular dynamics, and potential and surface driving geometric flows for the micromacro interface. For excessively large aqueous macromolecular complexes in chemistry and biology, we further develop differential geometry based multiscale fluidelectroelastic models to replace the expensive molecular dynamics description with an alternative elasticity formulation. 
 "Interestingly, complex shaped finite size domains of size L, in addition to undulating phases with lamellar and hexagonal ordering, were observed [8] [9] [12] [15] [2] [18] [19] [20] [21] [22]. The observed finite size domains in these systems have been shown to be due to competing interactions, especially shortrange steric, chemical mismatches and longrange dipolar interactions [23] [24]. "
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ABSTRACT: The formation of chiral nanopatterns on lowdimensional ionic assemblies via electrostatic interactions  [Show abstract] [Hide abstract]
ABSTRACT: Shapes and orientational deformation of a lipid monolayer domain have been analyzed taking into account the surface pressure, line tension, and electrostatic energy due to the spontaneous polarization and electric quadrupole density generated from the domain. The electrostatic energy due to the generation of spontaneous polarization and electric quadrupole density contributes to the formation of orientational deformation as the Frank elastic energy and spontaneous splay, respectively. Since the orientational configuration of the electric quadrupole density and inplane spontaneous polarization is dependent on the molecular chirality, and the positive splay deformation of electric quadrupole density is induced by the spontaneous splay, the bending direction of inplane spontaneous polarization depends on the chirality of constituent lipids. The electrostatic energy due to the inplane spontaneous polarization is dependent on the orientational deformation of inplane spontaneous polarization, and bends the domain shape towards the bending direction of the inplane spontaneous polarization. It has been demonstrated that the chiral dependence of the domain shapes of lipid monolayers originated from the chiral dependence of orientational structure due to the electric quadrupole density.