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Erschienen in:
Mechanics and Physics of Lipid Bilayers Kapitel lesen Erstes Kapitel lesen

2018 | OriginalPaper | Buchkapitel

Lipid Membranes: From Self-assembly to Elasticity

verfasst von : M. Mert Terzi, Markus Deserno

Erschienen in: The Role of Mechanics in the Study of Lipid Bilayers

Verlag: Springer International Publishing

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Abstract

In aqueous solution, lipid molecules spontaneously assemble into macroscopic bilayer membranes, which have highly interesting mechanical properties. In this chapter, we first discuss some basic aspects of this self-assembly process. In the second part, we then revisit and slightly expand a well-known continuum-level theory that describes the elastic properties pertaining to membrane geometry and lipid tilt. We then illustrate in part three several conceptually different strategies for how one of the emerging elastic parameters—the bending modulus—can be obtained in computer simulations.

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Vorheriges Kapitel Elasticity and Hereditariness
Nächstes Kapitel The Geometry of Fluid Membranes: Variational Principles, Symmetries and Conservation Laws
Fußnoten
1
Here we assume that a flat membrane is untilted—which is true for fluid phases, but not necessarily so for membranes in the gel phase.
 
2
During the workshop Jemal Guven pointed out that the additional required factor \(\cos \theta \) is the equivalent of what in a \(3+1\) foliation treatment of general relativity is called the “Lapse function” (Wheeler 1964).
 
3
Notice that if the monolayer leaflet were not fluid, a deformation that starts from a flat leaflet and ends up with one that has a non-vanishing Gaussian curvature cannot be isometric by virtue of the Theorema Egregium. Hence, this approach of writing the elastic energy by looking at the stretching away from a pivotal plane relies by construction on fluidity.
 
4
This is merely a consequence of the fact that the length \(\ell \), which pits curvature against tilt, is microscopic. On scales larger than \(\ell \), tilt therefore only enters as a minor correction to the overall bending physics of then problem.
 
5
Since \(T^2=T_p^2+T_q^2\), the tilt modulus along the edge (the q-direction) is just the prefactor of \(T^2\) in Eq. (124).
 
6
In simulations that can be achieved relatively easily by suitable boundary conditions.
 
7
Recall that we must measure the undulation spectrum \(\langle |\tilde{h}_{\varvec{q}}|^2\rangle \) over a sufficiently wide q-range to plausibly fit a spectrum, and that this spectrum decays rapidly with q.
 
8
Hu et al. (2013) discuss buckle fluctuations in a little bit more detail. They conclude that systematic fluctuation corrections exist, but that they are small for \(f_x\). They are not necessarily small for the force \(f_y\) acting along the buckle’s ridges, though.
 
9
One efficient construction method proceeds via the analytical expressions for position and angle of a buckle—Eqs. (139) and (140)—for mapping a flat membrane (leaflet-wise) into a buckled one. If a lipid’s center of mass in the flat configuration has coordinates \((x_0,y_0,z_0)\), map it to \((x(x_0),y_0,z(x_0))\) and rotate it around the y-axis by the angle \(\psi (x_0)\).
 
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Metadaten
Titel
Lipid Membranes: From Self-assembly to Elasticity
verfasst von
M. Mert Terzi
Markus Deserno
Copyright-Jahr
2018
Buch
The Role of Mechanics in the Study of Lipid Bilayers

Print ISBN: 978-3-319-56347-3

Electronic ISBN: 978-3-319-56348-0

Copyright-Jahr: 2018

DOI
https://doi.org/10.1007/978-3-319-56348-0_3

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