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Lipid membranes not only play critical roles in many cellular functions but are also unique in that they have properties of both fluid and elastic materials. While 2D elasticity theories, such as Canham–Helfrich–Evans, adequately capture the dominant energetics of membrane deformation, a full characterization of the 3D elastic response is necessary to account for the many modes of deformation and the role that lipid structure plays in determining the elastic energy. We use the stress–stress fluctuation (SSF) method to obtain local elasticity profiles of a simple water–dodecane interface and a lipid membrane from coarse-grained MARTINI molecular dynamics simulations. We validate the results from the SSF method through the explicit deformation method, which measures the change in the local stress tensor relative to a specific strain. Furthermore, we show that some expected symmetries of the elasticity tensor are locally broken due to the lateral fluidity of the interfacial systems and the physical constraint of mechanical equilibrium. Profiles of the lateral and transverse shear moduli show that the membrane is locally fluid, while the transverse shear modulus is locally nonzero, but its integral vanishes. We define the area, Young’s, and bulk moduli, as well as the Poisson ratio for a lipid membrane through the compliance tensor, and use the area modulus to estimate the position of the neutral surface and the macroscopic bending modulus. Our elasticity calculations provide critical insights into the local mechanical properties of lipid bilayers and unravel the role of lateral fluidity in the membrane’s elastic response.
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Microscopic elasticity from MD. I. Bulk solid and fluid systems
Computational modeling, such as molecular dynamics and Monte Carlo simulations, can be used to estimate the elastic properties of materials through various stress and strain relationships. Here, we demonstrate the effectiveness of the stress–stress fluctuation (SSF) method to estimate the elastic properties of simple van der Waals and molecular materials. The SSF method allows computation of the complete elasticity tensor from a single equilibrium simulation without requiring any type of deformation. While extensively used to characterize the elastic coefficients of crystalline solids and glassy systems, application of the SSF method to fluid systems and biomaterials has been limited. Starting with argon in the solid, liquid, and gas phases, we show that the SSF method gives elastic coefficients and moduli in excellent agreement with values obtained with the explicit deformation and volume fluctuation methods. Comparison of the elastic coefficients and bulk modulus for solid argon with previous computational studies and experimental data provides further validation of our numerical implementation. Beyond argon, we show that the elastic properties of molecular fluids simulated with the coarse-grained MARTINI force-field, which include multi-body interactions such as angle potentials, are also accurately captured by the SSF method. Moreover, the impulsive correction for truncated potentials is essential to obtain accurate values for these fluids and vanishing shear moduli. Our results highlight the broad applicability of the SSF method across a broad range of systems and lay the foundation for its use to characterize the elastic properties of complex molecular systems.
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- PAR ID:
- 10662857
- Publisher / Repository:
- American Institute of Physics
- Date Published:
- Journal Name:
- The Journal of Chemical Physics
- Volume:
- 164
- Issue:
- 2
- ISSN:
- 0021-9606
- Page Range / eLocation ID:
- 024110
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript
- Journal Article:
- https://doi.org/10.1063/5.0303843
