Finite element modeling of lipid bilayer membranes
A numerical simulation framework is presented for the study of biological membranes composed of lipid bilayers based on the finite element method. The classic model for these membranes employs a two-dimensional-fluid-like elastic constitutive law which is sensitive to curvature, and subjects vesicle...
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| Published in | Journal of computational physics Vol. 220; no. 1; pp. 394 - 408 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Amsterdam
Elsevier Inc
01.12.2006
Elsevier |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0021-9991 1090-2716 |
| DOI | 10.1016/j.jcp.2006.05.023 |
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| Abstract | A numerical simulation framework is presented for the study of biological membranes composed of lipid bilayers based on the finite element method. The classic model for these membranes employs a two-dimensional-fluid-like elastic constitutive law which is sensitive to curvature, and subjects vesicles to physically imposed constraints on surface area and volume. This model is implemented numerically via the use of
C
1-conforming triangular Loop subdivision finite elements. The validity of the framework is tested by computing equilibrium shapes from previously-determined axisymmetric shape-phase diagram of lipid bilayer vesicles with homogeneous material properties. Some of the benefits and challenges of finite element modeling of lipid bilayer systems are discussed, and it is indicated how this framework is natural for future investigation of biologically realistic bilayer structures involving nonaxisymmetric geometries, binding and adhesive interactions, heterogeneous mechanical properties, cytoskeletal interactions, and complex loading arrangements. These biologically relevant features have important consequences for the shape mechanics of nonidealized vesicles and cells, and their study requires not simply advances in theory, but also advances in numerical simulation techniques, such as those presented here. |
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| AbstractList | A numerical simulation framework is presented for the study of biological membranes composed of lipid bilayers based on the finite element method. The classic model for these membranes employs a two-dimensional-fluid-like elastic constitutive law which is sensitive to curvature, and subjects vesicles to physically imposed constraints on surface area and volume. This model is implemented numerically via the use of C1-conforming triangular Loop subdivision finite elements. The validity of the framework is tested by computing equilibrium shapes from previously-determined axisymmetric shape-phase diagram of lipid bilayer vesicles with homogeneous material properties. Some of the benefits and challenges of finite element modeling of lipid bilayer systems are discussed, and it is indicated how this framework is natural for future investigation of biologically realistic bilayer structures involving nonaxisymmetric geometries, binding and adhesive interactions, heterogeneous mechanical properties, cytoskeletal interactions, and complex loading arrangements. These biologically relevant features have important consequences for the shape mechanics of nonidealized vesicles and cells, and their study requires not simply advances in theory, but also advances in numerical simulation techniques, such as those presented here. A numerical simulation framework is presented for the study of biological membranes composed of lipid bilayers based on the finite element method. The classic model for these membranes employs a two-dimensional-fluid-like elastic constitutive law which is sensitive to curvature, and subjects vesicles to physically imposed constraints on surface area and volume. This model is implemented numerically via the use of C 1-conforming triangular Loop subdivision finite elements. The validity of the framework is tested by computing equilibrium shapes from previously-determined axisymmetric shape-phase diagram of lipid bilayer vesicles with homogeneous material properties. Some of the benefits and challenges of finite element modeling of lipid bilayer systems are discussed, and it is indicated how this framework is natural for future investigation of biologically realistic bilayer structures involving nonaxisymmetric geometries, binding and adhesive interactions, heterogeneous mechanical properties, cytoskeletal interactions, and complex loading arrangements. These biologically relevant features have important consequences for the shape mechanics of nonidealized vesicles and cells, and their study requires not simply advances in theory, but also advances in numerical simulation techniques, such as those presented here. A numerical simulation framework is presented for the study of biological membranes composed of lipid bilayers based on the finite element method. The classic model for these membranes employs a two-dimensional-fluid-like elastic constitutive law which is sensitive to curvature, and subjects vesicles to physically imposed constraints on surface area and volume. This model is implemented numerically via the use of C-conforming triangular Loop subdivision finite elements. The validity of the framework is tested by computing equilibrium shapes from previously-determined axisymmetric shape-phase diagram of lipid bilayer vesicles with homogeneous material properties. Some of the benefits and challenges of finite element modeling of lipid bilayer systems are discussed, and it is indicated how this framework is natural for future investigation of biologically realistic bilayer structures involving nonaxisymmetric geometries, binding and adhesive interactions, heterogeneous mechanical properties, cytoskeletal interactions, and complex loading arrangements. These biologically relevant features have important consequences for the shape mechanics of nonidealized vesicles and cells, and their study requires not simply advances in theory, but also advances in numerical simulation techniques, such as those presented here. |
| Author | Feng, Feng Klug, William S. |
| Author_xml | – sequence: 1 givenname: Feng surname: Feng fullname: Feng, Feng – sequence: 2 givenname: William S. surname: Klug fullname: Klug, William S. email: klug@ucla.edu |
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| Keywords | 02.70.Dh 46.70.Hg Subdivision surfaces Lipid bilayer mechanics Biomembranes 87.16.Dg 87.16.Ac 46.15.−x Cell mechanics Finite element Phase diagrams Membranes 87.16.Dg; 87.16.Ac; 02.70.Dh; 46.15.-x; 46.70.Hg Biomembranes; Lipid bilayer mechanics; Cell mechanics; Finite element; Subdivision surfaces Digital simulation Equilibrium shape Mechanical properties Calculation methods Finite element method Models Modelling Calculation Curvature |
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| Snippet | A numerical simulation framework is presented for the study of biological membranes composed of lipid bilayers based on the finite element method. The classic... |
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| SubjectTerms | Biomembranes Cell mechanics Computational techniques Computer simulation Curvature Exact sciences and technology Finite element Finite element method Lipid bilayer mechanics Lipids Mathematical analysis Mathematical methods in physics Mathematical models Membranes Physics Subdivision surfaces Vesicles |
| Title | Finite element modeling of lipid bilayer membranes |
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