Commun. Comput. Phys., 13 (2013), pp. 1093-1106.

Measuring the Spontaneous Curvature of Bilayer Membranes by Molecular Dynamics Simulations

Han Wang 1*, Dan Hu 2, Pingwen Zhang 3

1 LMAM and School of Mathematical Sciences, Peking University, Beijing, P.R. China; and Institute for Mathematics, Freie Universitat Berlin, Berlin, Germany.
2 Department of Mathematics, MOE-LSC, and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai, P.R. China.
3 LMAM and School of Mathematical Sciences, Peking University, Beijing, P.R. China.

Received 23 April 2011; Accepted (in revised version) 23 March 2012
Available online 21 September 2012


We propose a mathematically rigorous method to measure the spontaneous curvature of a bilayer membrane by molecular dynamics (MD) simulation, which provides description of the molecular mechanisms that cause the spontaneous curvature. As a main result, for the membrane setup investigated, the spontaneous curvature is proved to be a constant plus twice the mean curvature of the membrane in its tensionless ground state. The spontaneous curvature due to the built-in transbilayer asymmetry of the membrane in terms of lipid shape is studied by the proposed method. A linear dependence of the spontaneous curvature with respect to the head-bead diameter difference and the lipid mixing ratio is discovered. The consistency with the theoretical results provides evidence supporting the validity of our method.

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PACS: 87.16.D-, 82.70.Uv
Key words: Bilayer membrane, Helfrich free energy, spontaneous curvature, molecular dynamics simulation.

*Corresponding author.
Email: (H. Wang), (D. Hu), (P. Zhang)

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