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Molecular Dynamics Simulation of Membrane Continuum Models on Triangulated Meshes

Farnudi, Ali | 2024

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 56966 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Ejtehadi, Mohammad Reza; Seyed Reyhani, Nader
  7. Abstract:
  8. Lipid bilayers are one of nature’s solutions to confine and compartmentalize molecules and microorganisms. Usually, the thickness of the membrane is very small compared to the length scale at which it is studied. Therefore it is convenient to represent it with a 2-dimensional surface that has a stretch, shear, and curvature energy. Triangulated surfaces are the most popular discretization method to study the mechanical behavior of vesicles and fluid membranes since their elastic and bending moduli can be rigorously defined. Fluid membranes pose a particular challenge because they do not have a shear modulus. The dynamic triangulation algorithm is the state-of-the-art method developed to address this problem. In 1996, Gompper and Kroll calculated the curvature energy of dynamically triangulated surfaces with a uniform vertex distribution. In their method, the movement of mesh vertices was restricted to generate triangulated surfaces compatible with the curvature energy calculations. Since the meshed surface constantly changed, the Monte Carlo (MC) simulation method was adopted to implement the simulations. Unfortunately, this method is not compatible with Molecular Dynamics (MD) simulations. Continuum models like the Helfrich Hamiltonian are widely used to describe fluid bilayer vesicles. Here we study the Molecular Dynamics compatible dynamics of the vertices of two-dimensional meshes representing the bilayer, whose in-plane motion is only weakly constrained. We show (i) that Julicher's discretization of the curvature energy offers vastly superior robustness for soft meshes compared to the commonly employed expression by Gommper and Kroll and (ii) that for sufficiently soft meshes, the typical behavior of fluid bilayer vesicles can emerge even if the mesh connectivity remains fixed throughout the simulations. In particular, soft meshes can accommodate large shape transformations, and the model can generate the typical $\ell^{-4}$ signal for the amplitude of surface undulation modes of nearly spherical vesicles all the way up to the longest wavelength modes. Furthermore, we compare results for Newtonian, Langevin, and Brownian dynamics simulations of the mesh vertices to demonstrate that the internal friction of the membrane model is negligible, making it suitable for studying the internal dynamics of vesicles via coupling to hydrodynamic solvers or particle-based solvent models.
  9. Keywords:
  10. Molecular Dynamic Simulation ; Liquid Membrane ; Vesicle Shape Transformation ; MESH ; Triangulation Method

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