A multiscale approach to curvature modulated sorting in biological membranes

M. Mercker, M. Ptashnyk, J. Kuhnle, D. Hartmann, M. Weiss, W. Jager

    Research output: Contribution to journalArticle

    14 Citations (Scopus)

    Abstract

    Combining different theoretical approaches, curvature modulated sorting in lipid bilayers fixed on non-planar surfaces is investigated. First, we present a continuous model of lateral membrane dynamics, described by a nonlinear PDE of fourth order. We then prove the existence and uniqueness of solutions of the presented model and simulate membrane dynamics using a finite element approach. Adopting a truly multiscale approach, we use dissipative particle dynamics (DPD) to parameterize the continuous model, i.e. to derive a corresponding macroscopic model.Our model predicts that curvature modulated sorting can occur if lipids or proteins differ in at least one of their macroscopic elastic moduli. Gradients in the spontaneous curvature, the bending rigidity or the Gaussian rigidity create characteristic (metastable) curvature dependent patterns. The structure and dynamics of these membrane patterns are investigated qualitatively and quantitatively using simulations. These show that the decomposition time decreases and the stability of patterns increases with enlarging moduli differences or curvature gradients. Presented phase diagrams allow to estimate if and how stable curvature modulated sorting will occur for a given geometry and set of elastic parameters. In addition, we find that the use of upscaled models is imperative studying membrane dynamics. Compared with common linear approximations the system can evolve to different (meta)stable patterns. This emphasizes the importance of parameters and realistic dynamics in mathematical modeling of biological membranes.
    Original languageEnglish
    Pages (from-to)67-82
    Number of pages16
    JournalJournal of Theoretical Biology
    Volume301
    Issue number5
    Early online date9 Feb 2012
    DOIs
    Publication statusPublished - May 2012

    Fingerprint

    Biological membranes
    Sorting
    sorting
    Membrane
    Curvature
    Membranes
    Rigidity
    Model
    Dissipative Particle Dynamics
    Elastic Modulus
    Gradient
    Lipid Bilayers
    Lipid Bilayer
    lipid bilayers
    Nonlinear PDE
    Lipid bilayers
    Parameterise
    Linear Approximation
    Lipids
    Existence and Uniqueness of Solutions

    Cite this

    Mercker, M. ; Ptashnyk, M. ; Kuhnle, J. ; Hartmann, D. ; Weiss, M. ; Jager, W. / A multiscale approach to curvature modulated sorting in biological membranes. In: Journal of Theoretical Biology. 2012 ; Vol. 301, No. 5. pp. 67-82.
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    abstract = "Combining different theoretical approaches, curvature modulated sorting in lipid bilayers fixed on non-planar surfaces is investigated. First, we present a continuous model of lateral membrane dynamics, described by a nonlinear PDE of fourth order. We then prove the existence and uniqueness of solutions of the presented model and simulate membrane dynamics using a finite element approach. Adopting a truly multiscale approach, we use dissipative particle dynamics (DPD) to parameterize the continuous model, i.e. to derive a corresponding macroscopic model.Our model predicts that curvature modulated sorting can occur if lipids or proteins differ in at least one of their macroscopic elastic moduli. Gradients in the spontaneous curvature, the bending rigidity or the Gaussian rigidity create characteristic (metastable) curvature dependent patterns. The structure and dynamics of these membrane patterns are investigated qualitatively and quantitatively using simulations. These show that the decomposition time decreases and the stability of patterns increases with enlarging moduli differences or curvature gradients. Presented phase diagrams allow to estimate if and how stable curvature modulated sorting will occur for a given geometry and set of elastic parameters. In addition, we find that the use of upscaled models is imperative studying membrane dynamics. Compared with common linear approximations the system can evolve to different (meta)stable patterns. This emphasizes the importance of parameters and realistic dynamics in mathematical modeling of biological membranes.",
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    A multiscale approach to curvature modulated sorting in biological membranes. / Mercker, M.; Ptashnyk, M.; Kuhnle, J.; Hartmann, D.; Weiss, M.; Jager, W.

    In: Journal of Theoretical Biology, Vol. 301, No. 5, 05.2012, p. 67-82.

    Research output: Contribution to journalArticle

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    AU - Weiss, M.

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    N2 - Combining different theoretical approaches, curvature modulated sorting in lipid bilayers fixed on non-planar surfaces is investigated. First, we present a continuous model of lateral membrane dynamics, described by a nonlinear PDE of fourth order. We then prove the existence and uniqueness of solutions of the presented model and simulate membrane dynamics using a finite element approach. Adopting a truly multiscale approach, we use dissipative particle dynamics (DPD) to parameterize the continuous model, i.e. to derive a corresponding macroscopic model.Our model predicts that curvature modulated sorting can occur if lipids or proteins differ in at least one of their macroscopic elastic moduli. Gradients in the spontaneous curvature, the bending rigidity or the Gaussian rigidity create characteristic (metastable) curvature dependent patterns. The structure and dynamics of these membrane patterns are investigated qualitatively and quantitatively using simulations. These show that the decomposition time decreases and the stability of patterns increases with enlarging moduli differences or curvature gradients. Presented phase diagrams allow to estimate if and how stable curvature modulated sorting will occur for a given geometry and set of elastic parameters. In addition, we find that the use of upscaled models is imperative studying membrane dynamics. Compared with common linear approximations the system can evolve to different (meta)stable patterns. This emphasizes the importance of parameters and realistic dynamics in mathematical modeling of biological membranes.

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