A phase field approach in the numerical study of the elastic bending energy for vesicle membranes

Du, Qiang; Li, Chun; Wang, Xiaoqiang

doi:10.1016/j.jcp.2004.01.029

Cited by 365 publications

(370 citation statements)

References 35 publications

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“…For a brief review of these methods, in comparison with integral equation formulations, see [9]. Several groups have considered stationary shapes of three-dimensional vesicles using semi-analytic [10,15,56], or numerical methods like the phase-field [8,22,23] and finite element methods [25,43]. These approaches are based on a constrained variational approach (i.e., minimizing the bending energy subject to area and volume constraints) and have not been used for resolving fluid-structure interactions.…”

Section: Related Workmentioning

confidence: 99%

“…Consequently, the overall computational cost of the simulating in a fixed time horizon tends to be high, especially with increasing spatial resolution. For vesicles, the inextensibility constraint is typically enforced with an explicit penalty parameter [8,23,35] that introduces additional stiffness. In our explicit scheme, the inextensibility constraint is enforced using the tension as a Lagrange multiplier.…”

Section: Time Schemementioning

confidence: 99%

See 1 more Smart Citation

A fast algorithm for simulating vesicle flows in three dimensions

Veerapaneni

Rahimian

Biros

et al. 2011

Journal of Computational Physics

137

143

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Vesicles are locally-inextensible fluid membranes that can sustain bending. In this paper, we extend "A numerical method for simulating the dynamics of 3D axisymmetric vesicles suspended in viscous flows", Veerapaneni et al. Journal of Computational Physics, 228(19), 2009 to general non-axisymmetric vesicle flows in three dimensions.Although the main components of the algorithm are similar in spirit to the axisymmetric case (spectral approximation in space, semi-implicit time-stepping scheme), important new elements need to be introduced for a full 3D method. In particular, spatial quantities are discretized using spherical harmonics, and quadrature rules for singular surface integrals need to be adapted to this case; an algorithm for surface reparameterization is neeed to ensure sufficient of the timestepping scheme, and spectral filtering is introduced to maintain reasonable accuracy while minimizing computational costs. To characterize the stability of the scheme and to construct preconditioners for the iterative linear system solvers used in the semi-implicit time-stepping scheme, we perform a spectral analysis of the evolution operator on the unit sphere.By introducing these algorithmic components, we obtain a time-stepping scheme that, in our numerical experiments, is unconditionally stable. We present results to analyze the cost and convergence rates of the overall scheme. To illustrate the applicability of the new method, we consider a few vesicle-flow interaction problems: a single vesicle in relaxation, sedimentation, shear flows, and many-vesicle flows.

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Section: Related Workmentioning

confidence: 99%

Section: Time Schemementioning

confidence: 99%

A fast algorithm for simulating vesicle flows in three dimensions

Veerapaneni

Rahimian

Biros

et al. 2011

Journal of Computational Physics

137

143

View full text Add to dashboard Cite

show abstract

“…Computationally, phase field models can be used to simulate membrane curvature formation and evolution. 21 In the past decade, membrane curvature has been a popular research topic partially due to the fact that except for the curvature, there is very little other quantitative information associated with membranes and membrane protein/DNA interactions. Indeed, protein membrane interaction 39 and membrane curvature sensing have received much attention.…”

Section: Introductionmentioning

confidence: 99%

Multiscale multiphysics and multidomain models—Flexibility and rigidity

Xia

Opron

Guo

2013

The Journal of Chemical Physics

221

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The emerging complexity of large macromolecules has led to challenges in their full scale theoretical description and computer simulation. Multiscale multiphysics and multidomain models have been introduced to reduce the number of degrees of freedom while maintaining modeling accuracy and achieving computational efficiency. A total energy functional is constructed to put energies for polar and nonpolar solvation, chemical potential, fluid flow, molecular mechanics, and elastic dynamics on an equal footing. The variational principle is utilized to derive coupled governing equations for the above mentioned multiphysical descriptions. Among these governing equations is the PoissonBoltzmann equation which describes continuum electrostatics with atomic charges. The present work introduces the theory of continuum elasticity with atomic rigidity (CEWAR). The essence of CE-WAR is to formulate the shear modulus as a continuous function of atomic rigidity. As a result, the dynamics complexity of a macromolecular system is separated from its static complexity so that the more time-consuming dynamics is handled with continuum elasticity theory, while the less time-consuming static analysis is pursued with atomic approaches. We propose a simple method, flexibility-rigidity index (FRI), to analyze macromolecular flexibility and rigidity in atomic detail. The construction of FRI relies on the fundamental assumption that protein functions, such as flexibility, rigidity, and energy, are entirely determined by the structure of the protein and its environment, although the structure is in turn determined by all the interactions. As such, the FRI measures the topological connectivity of protein atoms or residues and characterizes the geometric compactness of the protein structure. As a consequence, the FRI does not resort to the interaction Hamiltonian and bypasses matrix diagonalization, which underpins most other flexibility analysis methods. FRI's computational complexity is of O(N 2 ) at most, where N is the number of atoms or residues, in contrast to O(N 3 ) for Hamiltonian based methods. We demonstrate that the proposed FRI gives rise to accurate prediction of protein B-Factor for a set of 263 proteins. We show that a parameter free FRI is able to achieve about 95% accuracy of the parameter optimized FRI. An interpolation algorithm is developed to construct continuous atomic flexibility functions for visualization and use with CEWAR.

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“…In this vein, a parametric approach is advocated in [6,4] while a phase field method is used in [17,18].…”

Section: Introductionmentioning

confidence: 99%

Dynamics of Biomembranes: Effect of the Bulk Fluid

Bonito

Nochetto

Pauletti

2011

Math. Model. Nat. Phenom.

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Abstract. We derive a biomembrane model consisting of a fluid enclosed by a lipid membrane. The membrane is characterized by its Canham-Helfrich energy (Willmore energy with area constraint) and acts as a boundary force on the Navier-Stokes system modeling an incompressible fluid. We give a concise description of the model and of the associated numerical scheme. We provide numerical simulations with emphasis on the comparisons between different types of flow: the geometric model which does not take into account the bulk fluid and the biomembrane model for two different regimes of parameters.

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A phase field approach in the numerical study of the elastic bending energy for vesicle membranes

Cited by 365 publications

References 35 publications

A fast algorithm for simulating vesicle flows in three dimensions

A fast algorithm for simulating vesicle flows in three dimensions

Multiscale multiphysics and multidomain models—Flexibility and rigidity

Dynamics of Biomembranes: Effect of the Bulk Fluid

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