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Poisson's Ratio and Young's Modulus of Lipid Bilayers in Different Phases.

Jadidi T, Seyyed-Allaei H, Tabar MR, Mashaghi A - Front Bioeng Biotechnol (2014)

Bottom Line: As an example for the coarse grained lipid model introduced by Lenz and Schmid, we calculate the Poisson's ratio in the gel, fluid, and interdigitated phases.Having the Poisson's ratio, enable us to obtain the Young's modulus for the membranes in different phases.The approach may be applied to other membranes such as graphene and tethered membranes in order to predict the temperature dependence of its Poisson's ratio and Young's modulus.

View Article: PubMed Central - PubMed

Affiliation: Department of Physics, University of Osnabrück , Osnabrück , Germany.

ABSTRACT
A general computational method is introduced to estimate the Poisson's ratio for membranes with small thickness. In this method, the Poisson's ratio is calculated by utilizing a rescaling of inter-particle distances in one lateral direction under periodic boundary conditions. As an example for the coarse grained lipid model introduced by Lenz and Schmid, we calculate the Poisson's ratio in the gel, fluid, and interdigitated phases. Having the Poisson's ratio, enable us to obtain the Young's modulus for the membranes in different phases. The approach may be applied to other membranes such as graphene and tethered membranes in order to predict the temperature dependence of its Poisson's ratio and Young's modulus.

No MeSH data available.


Related in: MedlinePlus

Snapshots of the lipid membrane in fluid phase as (A) initial configuration, (B) after increasing the bilayer size in y-direction by a factor of (1 + η), and (C) the relaxed bilayer fixing the membrane size in y-direction and variable x-direction. As a consequence of positive Poisson’s ratio for the bilayer in this phase, the membrane size in x-direction is reduced and equilibrated after a few number of MC steps. Lipid’s head beads and tail bead are shown in red and green, respectively.
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Figure 3: Snapshots of the lipid membrane in fluid phase as (A) initial configuration, (B) after increasing the bilayer size in y-direction by a factor of (1 + η), and (C) the relaxed bilayer fixing the membrane size in y-direction and variable x-direction. As a consequence of positive Poisson’s ratio for the bilayer in this phase, the membrane size in x-direction is reduced and equilibrated after a few number of MC steps. Lipid’s head beads and tail bead are shown in red and green, respectively.

Mentions: To determine both E and ν, we need to determine one of these elastic constants separately. Utilizing the periodic boundary conditions, we introduce a method to compute the Poisson’s ratio for the surface (Abedpour et al., 2010). The Poisson’s ratio is the negative ratio of the transverse strain changes divided by the axial strain changes in a body when it is stretched or compressed along the axial direction under the tension below the proportional limit. For the infinitesimal diagonal strains, the Poisson’s ratio can be replaced by the ratio of the relative length changes as νij = −ΔLi/ηjLi, where ηj ≡ ΔLj/Lj is defined as the fraction of the axial length change. Here i ≠ j and i = x, y, and z. In the method, we present here the length between neighboring lipids is rescaled by a factor of (1 + η) in axial direction, let say y-direction, and the subsequent change of the simulation box size in perpendicular directions, in this case x- and z-direction, are monitored. While keeping the rescaled box length (1 + η) Ly constant, for fixing the pressure in the simulations, the box dimensions are now allowed to fluctuate in only the x- and z-directions. When the initial mean lengths in x and z-direction were Lx and Lz, new mean values of Lx + ΔLx and Lz + ΔLz are reached after rescaling, by re-equilibrating the system for a few number of MC steps, see Figure 3.


Poisson's Ratio and Young's Modulus of Lipid Bilayers in Different Phases.

Jadidi T, Seyyed-Allaei H, Tabar MR, Mashaghi A - Front Bioeng Biotechnol (2014)

Snapshots of the lipid membrane in fluid phase as (A) initial configuration, (B) after increasing the bilayer size in y-direction by a factor of (1 + η), and (C) the relaxed bilayer fixing the membrane size in y-direction and variable x-direction. As a consequence of positive Poisson’s ratio for the bilayer in this phase, the membrane size in x-direction is reduced and equilibrated after a few number of MC steps. Lipid’s head beads and tail bead are shown in red and green, respectively.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4126470&req=5

Figure 3: Snapshots of the lipid membrane in fluid phase as (A) initial configuration, (B) after increasing the bilayer size in y-direction by a factor of (1 + η), and (C) the relaxed bilayer fixing the membrane size in y-direction and variable x-direction. As a consequence of positive Poisson’s ratio for the bilayer in this phase, the membrane size in x-direction is reduced and equilibrated after a few number of MC steps. Lipid’s head beads and tail bead are shown in red and green, respectively.
Mentions: To determine both E and ν, we need to determine one of these elastic constants separately. Utilizing the periodic boundary conditions, we introduce a method to compute the Poisson’s ratio for the surface (Abedpour et al., 2010). The Poisson’s ratio is the negative ratio of the transverse strain changes divided by the axial strain changes in a body when it is stretched or compressed along the axial direction under the tension below the proportional limit. For the infinitesimal diagonal strains, the Poisson’s ratio can be replaced by the ratio of the relative length changes as νij = −ΔLi/ηjLi, where ηj ≡ ΔLj/Lj is defined as the fraction of the axial length change. Here i ≠ j and i = x, y, and z. In the method, we present here the length between neighboring lipids is rescaled by a factor of (1 + η) in axial direction, let say y-direction, and the subsequent change of the simulation box size in perpendicular directions, in this case x- and z-direction, are monitored. While keeping the rescaled box length (1 + η) Ly constant, for fixing the pressure in the simulations, the box dimensions are now allowed to fluctuate in only the x- and z-directions. When the initial mean lengths in x and z-direction were Lx and Lz, new mean values of Lx + ΔLx and Lz + ΔLz are reached after rescaling, by re-equilibrating the system for a few number of MC steps, see Figure 3.

Bottom Line: As an example for the coarse grained lipid model introduced by Lenz and Schmid, we calculate the Poisson's ratio in the gel, fluid, and interdigitated phases.Having the Poisson's ratio, enable us to obtain the Young's modulus for the membranes in different phases.The approach may be applied to other membranes such as graphene and tethered membranes in order to predict the temperature dependence of its Poisson's ratio and Young's modulus.

View Article: PubMed Central - PubMed

Affiliation: Department of Physics, University of Osnabrück , Osnabrück , Germany.

ABSTRACT
A general computational method is introduced to estimate the Poisson's ratio for membranes with small thickness. In this method, the Poisson's ratio is calculated by utilizing a rescaling of inter-particle distances in one lateral direction under periodic boundary conditions. As an example for the coarse grained lipid model introduced by Lenz and Schmid, we calculate the Poisson's ratio in the gel, fluid, and interdigitated phases. Having the Poisson's ratio, enable us to obtain the Young's modulus for the membranes in different phases. The approach may be applied to other membranes such as graphene and tethered membranes in order to predict the temperature dependence of its Poisson's ratio and Young's modulus.

No MeSH data available.


Related in: MedlinePlus