Shape and stability of two-dimensional lipid domains with dipole-dipole interactions

Department of Physical Electronics, Tokyo Institute of Technology, Meguro-ku, Tokyo 152-8552, Japan.
The Journal of Chemical Physics (Impact Factor: 2.95). 01/2007; 125(22):224701. DOI: 10.1063/1.2402160
Source: PubMed


We study the general energy and shape of the two-dimensional solid monolayer domains with the dipole-dipole interactions. Compared with the domain energy without tilted dipole moments [M. Iwamoto and Z. C. Ou-Yang, Phys. Rev. Lett. 93, 206101 (2004)], the general dipolar energy is not only shape and size but also boundary orientation dependent. The general shape equation derived by this energy using variational approach predicts a circular solution and an equilibrium shape grown from this circle. In particular, the latter is composed of two branches: a translation-induced growth of all odd harmonic modes and a pressure-induced cooperative deformation by all even harmonic modes. The good qualitative agreement between our prediction and the experimental observations shows the validity of the present theory.

12 Reads
  • Source
    • "where N is the normal vector at x and H is the mean curvature. High-order curvatures have been extensively studied in the context of membrane bending analysis (Canham, 1970; Helfrich, 1973; Ou-Yang and Helfrich, 1989; Iwamoto et al., 2006). "
    [Show abstract] [Hide abstract]
    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 Navier-Stokes equations for the fluid dynamics, generalized Poisson equations or generalized Poisson-Boltzmann 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 continuum-discrete 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 micro-macro interfaces. The detailed balance of forces is emphasized in the present work. We further extend the proposed multiscale paradigm to micro-macro analysis of electrohydrodynamics, electrophoresis, fuel cells, and ion channels. We derive generalized Poisson-Nernst-Planck equations that are coupled to generalized Navier-Stokes equations for fluid dynamics, Newton's equation for molecular dynamics, and potential and surface driving geometric flows for the micro-macro interface. For excessively large aqueous macromolecular complexes in chemistry and biology, we further develop differential geometry based multiscale fluid-electro-elastic models to replace the expensive molecular dynamics description with an alternative elasticity formulation.
    Bulletin of Mathematical Biology 02/2010; 72(6):1562-622. DOI:10.1007/s11538-010-9511-x · 1.39 Impact Factor
  • Source
    • "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 short-range steric, chemical mismatches and long-range dipolar interactions [23] [24]. "
    [Show abstract] [Hide abstract]
    ABSTRACT: The formation of chiral nanopatterns on low-dimensional 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 in-plane 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 in-plane spontaneous polarization depends on the chirality of constituent lipids. The electrostatic energy due to the in-plane spontaneous polarization is dependent on the orientational deformation of in-plane spontaneous polarization, and bends the domain shape towards the bending direction of the in-plane 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.
    The Journal of Chemical Physics 04/2007; 126(12):125106. DOI:10.1063/1.2709644 · 2.95 Impact Factor
Show more

Preview (2 Sources)

12 Reads
Available from