7 research outputs found
A Computational Model of Protein Induced Membrane Morphology with Geodesic Curvature Driven Protein-Membrane Interface
Continuum or hybrid modeling of bilayer membrane morphological dynamics
induced by embedded proteins necessitates the identification of
protein-membrane interfaces and coupling of deformations of two surfaces. In
this article we developed (i) a minimal total geodesic curvature model to
describe these interfaces, and (ii) a numerical one-one mapping between two
surface through a conformal mapping of each surface to the common middle
annulus. Our work provides the first computational tractable approach for
determining the interfaces between bilayer and embedded proteins. The one-one
mapping allows a convenient coupling of the morphology of two surfaces. We
integrated these two new developments into the energetic model of
protein-membrane interactions, and developed the full set of numerical methods
for the coupled system. Numerical examples are presented to demonstrate (1) the
efficiency and robustness of our methods in locating the curves with minimal
total geodesic curvature on highly complicated protein surfaces, (2) the
usefulness of these interfaces as interior boundaries for membrane deformation,
and (3) the rich morphology of bilayer surfaces for different protein-membrane
interfaces
Hydrodynamic Coupling of Particle Inclusions Embedded in Curved Lipid Bilayer Membranes
We develop theory and computational methods to investigate particle
inclusions embedded within curved lipid bilayer membranes. We consider the case
of spherical lipid vesicles where inclusion particles are coupled through (i)
intramembrane hydrodynamics, (ii) traction stresses with the external and
trapped solvent fluid, and (iii) intermonolayer slip between the two leaflets
of the bilayer. We investigate relative to flat membranes how the membrane
curvature and topology augment hydrodynamic responses. We show how both the
translational and rotational mobility of protein inclusions are effected by the
membrane curvature, ratio of intramembrane viscosity to solvent viscosity, and
inter-monolayer slip. For general investigations of many-particle dynamics, we
also discuss how our approaches can be used to treat the collective diffusion
and hydrodynamic coupling within spherical bilayers.Comment: 32 pages, double-column format, 15 figure
The irreversible thermodynamics of curved lipid membranes
The theory of irreversible thermodynamics for arbitrarily curved lipid
membranes is presented here. The coupling between elastic bending and
irreversible processes such as intra-membrane lipid flow, intra-membrane phase
transitions, and protein binding and diffusion is studied. The forms of the
entropy production for the irreversible processes are obtained, and the
corresponding thermodynamic forces and fluxes are identified. Employing the
linear irreversible thermodynamic framework, the governing equations of motion
along with appropriate boundary conditions are provided.Comment: 62 pages, 4 figure
Arbitrary Lagrangian–Eulerian finite element method for curved and deforming surfaces: I. General theory and application to fluid interfaces
An arbitrary Lagrangian–Eulerian (ALE) finite element method for arbitrarily curved and deforming two-dimensional materials and interfaces is presented here. An ALE theory is developed by endowing the surface with a mesh whose in-plane velocity need not depend on the in-plane material velocity, and can be specified arbitrarily. A finite element implementation of the theory is formulated and applied to curved and deforming surfaces with in-plane incompressible flows. Numerical inf–sup instabilities associated with in-plane incompressibility are removed by locally projecting the surface tension onto a discontinuous space of piecewise linear functions. The general isoparametric finite element method, based on an arbitrary surface parametrization with curvilinear coordinates, is tested and validated against several numerical benchmarks. A new physical insight is obtained by applying the ALE developments to cylindrical fluid films, which are computationally and analytically found to be stable to non-axisymmetric perturbations, and unstable with respect to long-wavelength axisymmetric perturbations when their length exceeds their circumference. A Lagrangian scheme is attained as a special case of the ALE formulation. Though unable to model fluid films with sustained shear flows, the Lagrangian scheme is validated by reproducing the cylindrical instability. However, relative to the ALE results, the Lagrangian simulations are found to have spatially unresolved regions with few nodes, and thus larger errors